Church --of course is what in US is Anglican, in UK is Church of England(CofE)--chapel is another(any other?) protestant denomination, (in scotland is presberterian)

i don't know if there laws concerning churches other than CofE, but CofE membership (and baptism in CofE) was(is?) required for election to parlament, and other high offices of state--
(Disraeli's father had an arguement with his in-laws(or was it his father?) and as an act of spite, he had his son baptized in the CofE--Disraeli was not a big church goer- but because he was 'officially CofE' he could be prime minister.)

since being chapel bars you from (some) advancement-- to be chapel is to be of no account!

i think, current day, there aren't any laws about denominations in UK--there have been in the past--certainly it was illegal to be a 'Quaker'(member of the society of friends)-- and other demonimations were outlawed at other times as well (we'll gloss over RC--since my RC early childhood education filled me with such a one sided history, and was so filled with emotional, religious arguements, i still have trouble seeing straight)

if there are laws, (about religious worship) they seem generally not to be enforced... but unlike US, churches are taxed- and CofE gets most/some of its taxes rebated--though there is less and less state money going to support churches (especially small rural churches with dwindling congregations)the CofE is headed by the queen--and it is linked to crown, and country in a way that is hard to understand here in US...
(the recent brouhaha over an openly gay bishop (in US) was a cause for concern--the US anglican church (affiliated with CofE) is one of the largest 'collection' of anglicans--and if the CofE didn't accept the bishop, the US group was likely to split--and in religious circles, membership (and the assets the members hold collectively!) are a big deal. US anglican churches are relitively rich--(because they are untaxed)and the land and buildings are worth a small fortune)