To immigrate to the US based on this site you should put your first name to the last name field, and put FNU to the first name.
No first/last name
Some people in South India have only one name or all the names are
written in the column of a given name or surname and other field is
blank. If both the given name (first name) and surname (last name) are
not present in the passport, the consulate will write whatever names
are written in the passport as last name (even if that is your first
name), and write 'FNU' in the first name column. FNU stands for First
If you have more than one name but they are all written in one name,
and if you do not want 'FNU' as part of your name in the visa, you
should get your passport changed before applying for the visa.
To enter the UK I only found this forum, where someone allegedly put a '-' (dash) into the last name field and was granted immigration.
You should always read the form carefully, as details like this might be hidden in them. If in the end you cannot find the necessary answer give them a call or write them, so you won't end up declined because of your name.
It might also be a good idea that once you are able to enter the country to romanize your name (preferably without any acccents) and maybe also to give yourself a first or a last name (or split your name into two), as it will make things much easier in the long end, even if you dislike the fact that you will be known in a different name. In the UK for example you can just start calling yourself as you want to, but you might need to use a name change deed poll to get it also recognized by the government, or with some institutions, like banks.