In a smoke control area you can only burn fuel on the list of authorised fuels, or any of the following ‘smokeless’ fuels, unless you’re using an exempt appliance:
anthracite
semi-anthracite
gas
low volatile steam coal
Oil and kindling
You can use oil or other liquid fuels in specially designed or adapted fireplaces.
Kindling can sometimes be used but ask your council because there are different rules in different areas.