The general rule around carrying other passengers is that it is not allowed. You must not carry another person unless your bicycle is specifically designed for such purposes such as a tandem. s.24(1) of the Road Traffic Act 1988 states that carrying a passenger will constitute an offence. It says, “Not more than one person may be carried on a road on a bicycle not propelled by mechanical power unless it is constructed or adapted for the carriage of more than one person.” The maximum penalty for this offence is a fine of £200.
There are no legal restrictions on what can be towed by a pedal cycle. There are also no restrictions in law concerning carrying children in trailers. When it comes to carrying items, it's best to assume that unless the item can be carried without you having to take your hands off the handlebars, then it's ok. The Highway Code states that you must have both hands on the handlebars unless you are signalling.