How much are childminders in your area... a quick search reveals £4.50/£5 per hour, per child, though I only found a couple who gave any cost details so it could well vary more than that.
You have three children, two of whom are under 5, so you will be paying £100+ per day I would have thought.
£7.50 an hour to include everything is too low... I doubt you would find anyone prepared to care for your children at that rate, even if they did not have all three children at the same time all day.
A nanny share would be complicated, as you have 3 children and adding more into that will create issues with regard to transportation and equipment at your home, plus space consideration at your home. As Outraged says, finding someone with just one child to share with may work but you would not get much of a saving.
Nanny to work bank holidays, that may cost you more... some nannies may expect to be off work on bank holidays.
Could a combination of nursery and childminder work? Your baby plus DS in fulltime nursery, your daughter with a childminder before/after school and in school holidays. Problem though, cost... I expect it would be quite a lot.
Look at your budget for childcare, is it realistic?
A nanny who just cares for your children may well be possible but not at £7.50 an hour all inclusive. Your DS could still attend nursery but only for government funded sessions I suggest, to keep your cost down. Nanny could care for baby, DS and do before/after school care of DD. They could also do some light housework, such as children's laundry - which with 3 children will become a mountain in no time.
A full time, live out nanny (50 hours a week), could easily cost you £30,000 a year... probably more given you are in London.
A live-in nanny (or au-pair) could be a bit less but you are then having to provide a room and food/drink 7 days a week. You will lose the small amount of privacy you get at evening and weekends when having a live-out nanny. If you go for an au-pair, they probably will not have the baby experience and may well not be able to care for a baby all day long... it's hard work as you already know yourself.
A live-in nanny may be your lowest cost option, getting someone who is perhaps early on in their nannying experience, yet who you feel you can trust to care for your baby. However, their salary as a live-in nanny could easily be £350 gross per week, so costing you around £20,000 (including Employers NI) before you add in the other costs such as outings/activities, providing their board and lodgings, providing a car for them to drive perhaps!