Hi all,
Staying in Frankfurt for a month, then spending 4 days in Munich before going to the UK.
1. what is the cheapest way to get from frankfurt to munich?
2. what is the cheapest way to get from munich to london?
Thanks!

The least expensive way to get from Frankfurt to Munich (other than walking) is by train using a Bayern-Ticket. It will take a little longer because you can only use regional trains, but at €19 for one person, €27 for up to five people, you can't beat the price.

Someone else will have to answer the Munich to London question.

The Bayern-Ticket is valid for unlimited travel on regional trains in Bavaria for a day (after 9 AM weekdays, from midnight weekend days).

If you leave Frankfurt heading for Würzburg, the first stop in Bavaria is in Kahl, just beyond Hanau. You can start using the Bayern-Ticket in Kahl, but you will need an RMV ticket from Frankfurt to Kahl. From anywhere in downtown Frankfurt that will cost €6,60 per person.

German Rail does have a special fare from Frankfurt to London of €69. This includes travel from Frankfurt to Köln via DB (ICE or IC) and travel from Köln to Brussels by either DB or Thalys. Travel from Brussels to London is via Eurostar.

Of course, you have to get to Frankfurt, but you already know how to do that, economically, in reverse.

thanks very much for that... was a bit sketchy on the train system in germany even after doing the research, so that really helped to clear things up! thanks!

The cheapest way from Munich to London is likely to fly on a budget carrier. For instance, I just checked easyJet, and it is €50.99 on Aug 1. Mind you this is for a late night flight to London Stansted, but it does include all taxes.