TV's signals in the UK are in the PAL I format whilst in Singapore they are in PAL B/G.
Your old TV may or may not work in Singapore dependening on whether it can also accept PAL B/G.
Likewise your new TV will work direct from the normal aerial socket in the UK if it can also handle PAL I.
However, in both cases you you need to check the manual. Dealers will tell you that your TV is "multi-format" but this does not mean that it can accept all formats.
If they don't accept the correct format for the country that you are in then you need to get some sort of convertor. Alternatively, you may be able get reception from a cable or satellite receiver or a VCR which allows output using the A/V connectors (these are the red, yellow and white sockets on your equipment).