LHR terminal 3 to terminal 4 arrivals?
 

We arrive at terminal 3 at LHR but have to meet another couple and our driver at terminal 4 arrivals.
Was is the easiest way to do this with luggage?

Easiest way is to take the Heathrow CONNECT to T4 - but how are you leaving LHR as you'll probably have to pass through T3 in order to do so

Is the connect to T4 bus or train?
Airport Connections Car service is picking us both up at terminal 4 as our flight comes in 45 minutes earlier than the others and he will only do 1 pickup spot.

The Connect is a free train. It's really the only option for you.

Go through immigration and customs, then follow the signs. At the T4 station, just take the lift to the arrivals level.

You will need to leave the luggage trolley you obtain at T3 at the entrance to the platform to the Connect train, then fetch another at the T4 end. You can't take trolleys onto the actual platforms.