Hi SC, one can still eat well cheaply in London, e.g. their cornish pie is about £2+ and it's big enough to work as brunch. And surprisingly, I find some of their groceries quite cheap (cheaper than in Sg if you're earning pounds), e.g. a large pack of baked waffles or some other pastry like thosai costs £1.80 which can last for 3 meals! These were prices that I saw last Nov.
Stonehenge is good to see, just stand outside the fence and save the exorbitant entrance fee.
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You can do the same for those Windsor castle, etc. ...just admire from outside. I like Bath...it's such a quaint town with little houses build close together...it had a very nice Thai restaurant many years ago but I'm not sure if it's still there. Have fun!
ps: sorry, I've no info on how to get to those places, as I'd rented a car and drove out from London many years ago.