Okay, a lot depends on the size of the trailer, if you're going to use it after sunset, and the year of manufacture of the trailer (yes I had to read up on this quickly to remind myself)
The definitive guide is
HERE the Road Vehicle Lighting Regulation Act 1989
The most important point for you is "6(4) The exemption from the need for a small trailer to be fitted with any stop lamp or direction indicator when those on the towing vehicle are visible to an observer 6 m behind the trailer will not apply to a trailer manufactured on or after 1st October 1990."
Basically if you can see the lights on your car, it's not a new trailer (without a tag not sure how they'd tell) and you're not using it at night you should be okay, but you DO still need to have the red warning trianle reflectors on the back of the trailer (and a reg plate if it obscures yours)
Depending on the size of the trailer (and remember, if your trailer is loaded can your lights still be seen) a different set of regulations apply, but basically: "(5) No trailer manufactured before 1st October 1990 *this may be on your tag* is required by regulation 18 to be fitted with any stop lamp or direction indicator whilst being drawn by a motor vehicle fitted with one or two stop lamps and two or more direction indicators *basically meaning, your car* if the dimensions of the trailer are such that when the longitudinal axes of the drawing vehicle and the trailer lie in the same vertical plane *it is towing it* such stop lamps and at last one direction indicator on each side of the vehicle *your cars rear lights* are visible to an observer in that vertical plane from a point 6 m behind the rear of the trailer whether it is loaded or not. *if someone is stood behind the trailer can they see the lights on your car*
I hope that helps, I added on the bits in "*" because at 2am this stuff can seem a bit heavy
