Going to london, for a quick getaway for 4 days. Looking to see if there is any good group rides I could join. Probably need to rent a bike since I don’t want to deal with taking my ritchey breakaway unless no other options. Staying at Rad Blu Mercer Street as far as location. Wife will let me get out for a 3 hour ride or so. Also any decent shops to take a look at? Went to Condor last time I was there. Thanks!
In terms of bike hire, “On Your Bike” in London Bridge hire out Trek bikes (low- to high-end). Not used them myself.
Rapha group rides are about 2 minutes walk from where you are and there are tons of other cycling clubs, especially around Hackney (eg. Pretorious, eastlondonvelo.cc, Vicious Velo) and on the border of Surrey. You could also just head out to Richmond Park yourself - so many cyclists riding there everyone looks like they are on a club run.
Fixed is a big thing in London if that floats your boat (lfgss.com).
If you want a shop full of bike porn go to Bespoke on Farringdon Road. Leave your credit card in the hotel though.
Having grown up in London for the first thirty years of my life I would recommend waterproof jacket and thermals - pretty good chance you will get wet and/or cold on a ride. Spend the time enjoying the city rather than riding - although there is a huge riding culture around London it is way different than most other cities, so unless you are very sure of yourself and understand the British drivers attitude you would be safer off maybe going for a run in one of the many fabulous parks in the city.
Depending on the weather (currently nice but iffy at the best of times), surrey hills are nice (box hill and others nearby are weekend favorites) and fit the time allowance… start from richmond park and head southwest from there but probably need to find a group to tag along with as you may get a bit lost…