With respect my friend I think you need to be a little less sensitive. Arye is asking about ways to see and experience Britain. I'd be surprised if he wants a guide as to how to duplicate the Israel experience in the UK. London is a 'given', but the rest is hugely varied and I think my quip about Watford still has validity despite your response.( It is something of a northern UK 'truism' that many in 'That London', know little of life, or indeed geography, 'north of Watford'.)
Oxford and Cambridge both have their merits, obviously, and some interesting attractions, but it's also arguable that once you've seen one Oxford quad, or one set of incompetent Cambridge students falling out of punts.. you've seen them all..
Also, the fact that I mention pubs and clubs is simply information. I am not advocating a pub crawl.. That seems to be more a function of your apparent dislike of alcohol. In Liverpool the Cavern in particular ought to be on the itinerary of anyone with an interest in popular music. It is open from midday to late everyday, has free admission, live music, lots to see, and a bar from which the purchase of alcohol is entirely optional. It is visited by people of all ages, from all cultures and all countries.The thing is , there is no compulsion to enter any establishment just because I have mentioned it and there is no compulsion to consume alcohol if you do. All UK pubs serve soft drinks or coffee/tea. I also mentioned two cathedrals but I'm not religious at all, nor am I advocating conversion to Christianity. They are simply valid attractions.
Disappointingly, there is no bar in Liverpool Central Library...
Mull