Hi OP- I visit Guys (from several hours outside of London) several times a year, and need my partner to drive me due to ill health. I've also had two non-urgent day surgery procedures there this year as an oupatient so can give you my two pence' if helpful.
So far as we are aware the closest and readily available parking is the NCP (London Road) which is a short walk from the hospital, probably not much more than you would be walking if you got the tube. We always have to pre-book online to ensure we actually get a space and i must say it is always very busy and is a very tight car park space wise (just something to be aware of in case you have a large car or a parking phobia). Downsides are that it's bloody expensive, and even more so based on the fact you are not going to accurately be able to estimate how long you will need to space for.
As an example for a just standard appointment with no surgery we quite often have to book the car park for three hours to accommodate long waiting times/walks to and fro/wanting to get there well in advance of the appointment so as not to be late.
WIth regards to a day surgery, as i mentioned, i have had two this year both not complex procedures and no issue whilst under but the average time all on from 'checking in' at the time they state to actually getting back in the car, will be virtually a whole day.
On arrival patients will be checked in at the same time so AM patients all arrive at 8am ( or whenever)- there is then a wait to go in to see the nurse and have vitals taken, change into gowns, compression stockings and go through any medical issues or the procedure. Then there will be a wait to speak to the anaesthetist. After this another wait to be called in and plonked on a bed, probably another wait before you are wheeled into surgery itself, that will be an hour, and then some time in a bed in recovery while you come around from the GA, and you are then dressed and moved to the recovery suit ( glorified waiting room) where you will need to evidence that you can eat and drink, and use the toilet. After this the nurses will discharge. If you are unlucky and end up at the bottom of the surgery order list and go in last this can really be a long day as you are literally waiting for others to go in and come out of the theatre so you can go next. As a rough guide my last two surgeries were - got there 7:30am for an 8pm start, surgery happened just before midday, left at approx half 3.
Sorry for the essay but just trying to get across how it really adds up with the NCP car park, plus there's the congestion charge to pay on top. You can usually get a 10% discount code for the car park by googling which knocks a little off but is is pretty pricey. You don't mention your daughters age so i don't know if you plan on taking her and waiting, if she's not a child and can get there alone you could just turn up for the back end of the timescale so you can pick her up and keep costs down. Just bear in mind she won't be allowed her phone on her for the vast majority of this experience, it will be in a locker until she leaves so it gets tricky as you can't text and say " im going in now" or anything. You can call the admissions team who can update you though.
If your daughter has had a GA she won't be allowed to leave unless someone collects her, I don't know if you are aware. If you/she are London based a taxi might be a better idea. Guys does have a dropoff point but it is always full and a nightmare and as i said, she would need to be collected in person and you can't actually park there.
Wishing her the best of luck and a quick recovery- as someone who does it frequently i must say that some people are absolutely fine afterwards really, they scoff down the tea and sandwich and are up and about waiting to go. I suppose it depends how well you do with the GA and what you've had done and that's unique to the person really.