Agree with the recommendations above from Lady Lucy. I both taught in Surrey and sent my children to school there so am quite in the loop... I hope this helps:
There are absolutely tonnes of good preps. A few are quite old fashioned and friends moving out from London used to the generally very innovative preps with high quality enthusiastic teachers found some of the preps down in Surrey/Hampshire a bit behind the times or more sleepy.
Avoid The Royal - it has been really struggling and re-branded/re-configured itself so many times to keep going. Not heard good reviews and would go for a more stable and well-regarded place.
In terms of your question about where do pupils go after these schools, obviously look at the leavers' destination pages of the website. There is huge choice in Surrey but it will mean more travelling than you are used to in London. Lots of senior day pupils get the train to their school and it is a fun social time.
Senior schools are either 11+ or 13+:
11+ schools: Churcher's, Guildford High (girls), St Cats (girls), Tormead (girls), Prior's Field (girls, less academic), King Edward's Witley, Royal Grammar School (boys), Farnborough Hill (girls), Salesian (boys)
13+ schools: Charterhouse, Cranleigh (or send away to other public boarding schools)
Either 11+ or 13+: Seaford College (good for SEN), Frensham Heights/Beadales (alternative, liberal schools), St John's Leatherhead, Epsom College, Reeds (boys)
Cobham/Esher area: Danes Hill (known as quite flashy but v strong academics, fun school), Feltonfleet (great easy location, traditional prep, good size and successful), Downsend, Parkside boys, Ripley Court
Guildford area: Guildford High girls (academic, similar style to Putney High etc in London), Tormead girls (Latymer Upper head has just taken over), Lanesborough boys (super reputation), Rydes Hill
Godalming area: St Hilary's (but watch out for their narrow leaver's destinations), St Catherine's Bramley girls (v v traditional but right for the right families), Aldro (7+ traditional but going co-ed)
Haslemere/Liphook: Highfield & Brookham (really popular suddenly, amazing grounds, hot destination for Clapham parents it seems at the moment!), St Edmund's (goes to 16 now, known as being less academic), Amesbury (traditional fun prep), Churchers (all through, reasonably academic), St Ive's (used to be good but struggling with numbers, good leaver's destinations)