Here, at least, are links to commercial services:
http://www.chauffeurservice-hamburg.de/eng/company.html
http://www.chauffeur-in-hamburg.com/index/getlang/en

Thanks dfourh
Have you used either of these?

Tuppy...I salute you and anyone who takes the time and shows the interest in visiting a military cemetery. It's always been one of my travel goals anywhere in the world. I also visit K-Kamps to pay respect for those who were murdered during the Holocaust. I find it all very rewarding.Good luck in your quest.
stu

Stu,
How very kind. I shall be paying my respects to an RAAF Navigator, flying out of East Kirkby, England, shot down over Brunswick in 1944. He was to marry my aunt, an Aircraft Woman in the Australian RAAF. They were tragically killed 5 weeks apart. My grandmother mourned her all her life. I cherish my aunt's engagement ring.
Sherri

such a very sad story, Sherri... your visit will be both meaningful and therapeutic for you.

I wish I could help in recommending a driving service. Dfourth's links should be helpful for you. (My longtime best Australian buddy lives in Kingscliff, just south of the Queensland border).

Good luck and good connections.
stu tower

Just as a benchmark when checking prices with chauffeur services:
Your trip is roughly 200kms altogether for which the regular Hamburg cabs website gives an estimate of roundabout €220. As for rides outside the Hamburg city limits fares are not fixed, you have to agree on a price with the driver before you jump into the cab.
If all quotes are a bit too expensive (and it IS really expensive to do such a stunt compared with renting a car for a day plus costs for fuel) you can still train to Soltau (mildly inconvenient with 2 changes) and take a cab from there.

Thanks so much Cowboy. Had considered the train Soltau, but after consulting the directory, decided the two changes (and a taxi) too much of a risk.
Renting a car seems to be the sensible solution.

Tuppy - this may be of interest [I made a similar visit last year]

http://www.fodors.com/community/europe/non-war-cemetery-allied-war-graves-in-france-and-elsewhere.cfm

Best wishes for your trip.

farrermog - thank you. How very wonderful for your aunt. Memories are such deeply personal emotions.

For those interested in RAF and RAAF remembrance. The Church of St. Clements in London, (dubbed the RAAF church) turns daily a page which lists the names of those fallen in WW2. This Church remains as it did post WW2 London bombings, deeply scarred and pitted on its exterior.
The floor shows the insignia and motto of each squadron.

My aunt, an RAAF Aircraftwoman is buried in the small War Cemetary in Townsville, north Queensland, Australia. Townsville was a large aircraft base for Australians and Americans during WW2 and was bombed on three separate occasions by the Japanese.

Tuppy

My aunt served in the WAAAF during the war (holding back the Japanese from Melbourne my ex Navy uncle used to say). She has never been to Europe, had only the scantiest details of the resting place of her old boyfriend (to whom she was to be engaged) until my making enquiries at her request about five years ago, and was very pleased to receive my call from a phone box next to the churchyard (even at two in the morning in Australia).

Although the circumstances of your airman are different - shot down over the enemy's own territory and taken to a dedicated military cemetery - I am taking the liberty to mention here just a few examples from my aunt's case to demonstrate the stories which might be revealed about any of those fateful actions (particularly with the cooperation and generosity of others, a bit of luck, and the great advantage now of the internet).

For example -

after placing an enquiry on the internet 63 years after the event I was contacted by a bloke from England who just happened to be putting together the story of the aircraft and visiting the grave of the final crew in France the very next week - his father, who had only recently died, had been a member of the previous crew who had all survived the war and worked together for about 40 years in a firm in London owned by the family of the pilot!

from Australia I eventually put him in contact with another bloke in England, the son of the only survivor of the aircraft's final flight - the grave contains the all too usual full Lancaster complement of seven crew, but there was another person along for that particular flight and, as luck would have it, he was blown out of the aircraft, survived, became a POW, and lived for another 50 years, regularly visiting the site and meeting locals who had remembered the events. We have copies of clandestine photographs of the wreckage and the burials next day.

how the fateful flight unwound - late in taking off, so they attracted the full brunt of the German nightfighter effort in what turned out to be most unfavourable conditions for the bombers - no cloud cover under a full moon and adverse winds. That night a crewman on another aircraft on the same mission won the VC for crawling onto a wing and trying to douse an engine fire.

we even know the likely identity of the German pilot - also someone's son, brother, boyfriend - who shot them down, where he came from (a Ruhr city which knows the cost of war) and what happened to him (killed a few months later flying in support of a German counter-offensive after the Allied landings).

FWIW I'd be inclined not to rule out visiting the Becklingen cemetery by public transport, although granted you would also have the taxi connection to make as well - but western European ground transport systems seem to connect fairly efficiently and the frequency of services is also a plus compared with here in Australia - my war grave visit was made as a day trip (400 km round trip) from Paris (where admittedly I had 12 nights) and involved train/ bus connections - three hours out and four back after a few on site - and I didn't leave my apartment until late morning.

To top off what was a most memorable day, as I was waiting for a bus after visiting the grave two fighters suddenly appeared out of nowhere behind me and roared off down the valley towards the sunset and the very airbase from which German nightfighters had flown all those years ago.

And, as it happened, the next week when in London I attended a delightful (and cheap!) classical concert at St Clement Danes, which is as you have mentioned the Air Force church, and which was badly damaged by German bombing in 1941.

I'm sure your visit will be just as memorable!

farrermog,
I have goosebumps!!!!! Thank you for sharing these experiences. Have you read, "No Moon Tonight" by WW2 Lancaster navigator, Don Charlewood? Available from Australian libraries.

I shall again at St. Clements in August 2013! Aren't classical concerts in churches in England just wonderful?

Included in this trip is planned 3 weeks in England, with a visit to the memorial at East Kirkby airfield. I should end this now. Again, many thanks.