Thisdoesnotgeteasier, if you decide that you really want Surbiton, you should tell them you would accept the place if offered.
Girls on the wait list will all be good enough, they really would not put girls on a wait list if they thought they would not thrive, and there wont be much between them. If SHS then have a place to offer they would prefer to offer it to someone who will take it, rather than offer it three or four times, wait two weeks each time, until it is finally accepted.
Tell them early and then once you know what else you have been offered, give them the deadlines by which you have to put down a deposit for another school.
There is no reason to repeat anything they already know about your child, but if there is something new, like her best friend/neighbour is going which means she will settle more quickly and have someone to share a bus journey with, there will be no harm in evidencing your keenness.
If you want to continue being considered, I would follow up every couple of weeks with a short email, confirming you are still interested and asking if there has been any movement. The big movements will happen on National offer day which is usually just before deposits are needed, and then just before the start of the summer term when you become liable for a terms fees. But circumstances change and places can come up all the way through to the first day of term. (If really late I would ask if they can help you a bit financially, as they will have the deposit/fees from the drop out.) Especially SHS, as a change in circumstance for someone with a place at SPGS can trickle down through PHS and more, to SHS.
And similarly anyone who is not going to accept an offer should phone the school as soon as they can. It makes management of the wait list easier for the Registrar. They may then ask you to put it in writing, but our experience was the phone call was enough.
DD played sport with girls from SHS. Nice girls. It seemed like a nice school.