You could try e.g. Guildford, which has three very good independent girls schools St Catherines, Guildford High, and Tormead.
All three run from 4-18.
Prep schools generally don't prep for grammar, but for senior independent schools.
There is a well-regarded state comp, George Abbott, you will need to be within about a mile of it, but check the exact rules on this. 38 minutes into Waterloo, then two easy and not absurdly crowded stops on the Bakerloo Line to Piccadilly Circus.
If you do want to be in George Abbott catchment you will be over a mile from the station I believe, downhill by bicycle to the station in the morning though.
Gordon's School is located in West End, and is a pseudo-private state school for the fortunate few who can get within its tiny catchment. Results extremely good for a (pseudo-)comprehensive.
If you see rightmove, you can see that properties are advertised with the distance from the front gate of Gordon's! www.rightmove.co.uk/property-to-rent/find.html?searchType=RENT&locationIdentifier=POSTCODE%5E1492429&insId=3&radius=0.5&displayPropertyType=&minBedrooms=&maxBedrooms=&minPrice=&maxPrice=&maxDaysSinceAdded=&retirement=&sortByPriceDescending=&_includeLetAgreed=on&primaryDisplayPropertyType=&secondaryDisplayPropertyType=&oldDisplayPropertyType=&oldPrimaryDisplayPropertyType=&letType=&letFurnishType=&houseFlatShare=false
The first house there, at £2.5k PCM, is a little small IMO for the money, but you are paying for the school.
Basically what you would do here is rent that house till your older daughter has gained admission to the school, and then subsequently you can move to somewhere closer to a station for commuting to London and the younger sibling would get admittance based on sibling policy.
Coworth-Flexlands the local prep www.coworthflexlands.co.uk/ would probably have spaces immediately.
For the first year till you've got your school place, you'd probably drive to Brookwood station, from where it's 36 minutes by train to Waterloo.
Subsequently you could move somewhere within walking distance of Brookwood station, or Woking station, which has a 27 minute journey time into Waterloo, and is still a reasonable journey for your daughters to Gordons.
In terms of grammars there are quite a few in London, but admission is in each case highly competitive, and it's much easier to buy access to a comprehensive-for-the-rich like one of those above, than to buy access to a super-selective grammar school. Some parents spend five years torturing their children with four hours of daily 'which ridiculous shape comes next?'-type questions, but it's no guarantee of success; if your older daughter has done a CAT test in her current school, then that will gives some indication of her chances of success - scores of 115+ in all areas would be a starting point, less than that and you probably won't succeed with admission to super-selectives.
Kendrick school in Reading is a very good (girls) grammar school, and there's a list of acceptable postcodes for applying on their website. There are also four (mixed) grammar schools in Slough, each with differing admissions policies (one is Catholic), and there is an area between Reading and Slough of overlap between these.
Reading itself is a bit urban and gritty, but it has very fast trains to London (29 minutes). It's 10 minutes from there to Piccadilly Circus, though add in time to change trains and walk at the other side.
Reading probably has more crime than all of Singapore, though that's not saying much really, and there's a lot of shops and amenities.
Within a few miles of Reading you've got some proper millionaires hideouts, like Pangbourne and Henley (which would be well within catchment for Kendrick), although the journey time is inevitably much longer.
Something like this, however, is a short cycle ride from the train station, and therefore just under an hour door-to-door to Piccadilly Circus: www.rightmove.co.uk/property-to-rent/property-25034847.html
It goes without saying that you wouldn't find anything like that in London for that money.
Failing Kendrick admittance (and it is very competitive), the Abbey is the local girls private school www.theabbey.co.uk/ but there are dozens in easy admittance.
Obviously the state school system in the UK favours the rich and mobile, and moving in Y5 you've got the optimum opportunity to cherry pick the very best education money can't buy (you just have to buy/rent the house!), prior to Y6 applications and then hopefully a sibling policy to get in younger sister in the future.
Counties with more comprehensive (ahem) grammar school systems are essentially Kent and Bucks, and in those you need to be bright, but not exceedingly so to pass, since the entire county is covered. Main commuter towns would be Amersham (relatively slow train, 37 minutes), Beaconsfield (22 minutes, very affluent town), and High Wycombe (a bit grotty, 30 minutes), all into Marylebone. In Kent, you are probably looking at Sevenoaks (very expensive, but the train is direct to Charing Cross (in 35 minutes), which is essentially Piccadilly Circus, so need to take a tube, just walk).
If you venture further out into the less affluent parts of Kent, property prices are lower, and the high-speed rail link is now in place. 18 minutes from Ebbsfleet Int'l to St Pancras, and a short drive from somewhere like this: www.rightmove.co.uk/property-to-rent/property-36064561.html Although a bit of a trek to school.
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