You need to know where they are likely to have had their death registered to make initial enquiries. If it is a death within the last year or so you will have to contact the local register office for birth marriage and death and ask them to look at their index.
If it was earlier you can look at the index online at ancestry.co.uk up to 2005 (I think), it;'s a national index, but you do need to pay a fee to join, actually you could use the pay as you go option in findmypast.com just for the one search.
Another way, if you knew where they were probably last living, would be to look at the local death notices in the local paper, or ring local Funeral Directors, though they are not able to give out much info.