Hi garbfink
Finding burials and cremations has always been tricky especially in cities since the 1850's but it is an improving pircture.
So first of all you've got parish registers.
Then when the parishes stopped using their churchyards you need to look for cemeteries either privately owned or minicipal.
For details of these look on the internet for the cemeteries page of the local council website. You may find it's the council or in some instances the parish council who are responsible for maintenance. Some charge for look-ups.
Some councils have started transcribing their own databases.
Some older cemeteries have 'Friends of' organisations who look after the registers and can do look-ups. Some charge for look-ups.
Then look to sites such as
www.deceasedonline.comIt's free to search but you have to pay to see more details.
There's a useful topic here
http://www.rootschat.com/forum/index.php?topic=403485.0it's relevant to London & Middlsex but gives an idea of what you need to know for elsewhere
It always helps to have the death cert for exact dates of death, if you don't have this try probate records
https://www.gov.uk/search-will-probate