Most uk library have activities for children at library’s, especially during school holidays.
For example I can see Derby library has kids story time events, craft events, stem kids tech events all just in the next few weeks.
Ideal for your 5 year old soon. You can generally take older child and then play and read with younger one nearby.
Most libraries also have casual craft areas, or duplo or just loads of books for each age so they can just browse for an hour. There will
be lots of touchy feely type books for 2 year old. The story times are usually about 45mins and ingaging for toddlers with puppets and movement
I think most 2 and 5 year olds are the same as yours. Mine at 2 literally would not sit still, and still doenst tbh now. But at 2 I would just take pram or back sling and walk them as much as possible, then into pram when they gave up. You can usually hook balance bike easily to pram or underneath so only letting them use in safe park areas away from cars.
Ikea is ideal in winter. It’s massive, and dry during cold rain to wear them out. You can wander around with trolley to put them in when needed, but a walk wears them out, most they have a play area for free with cafe next door so you can sit with book and coffee and they go wild for free in view. Kids food there is cheap and they do ice cream for about £1 ( bribe them to leave). The hour drive there and back, and you have passed a good few hours.