Your description would indicate that the tail lights are wired wrong.
To fix it, you will need a test light, a DVOM, some masking tape, a pen, and a helper.
1. Take out both tail lights and remove all the bulbs.
2. Check the brown wire continuity to ground with the DVOM. Hook one lead of the DVOM to the negative battery post, and the other to the brown wire on the tail light. If you don't have continuity, trace out the wire and repair as needed.
3.Hook the wire on the test light to the brown lead, turn on the park lights, and touch the test lead spike to each wire until it lights. Label that one "park lights."
4. Turn on the turn signal for that side, and touch each wire with the test light spike until one starts flashing. Label that wire "turn signal."
5. Have your helper step on the brake, and touch each wire until the test light illuminates. Label that wire "brake light."
6. Put the car in reverse, and verify with the test light that the remaining wire lights the test light when touched with the spike. Label that wire "backup light."
Now, on to the buckets.
1. Using the continuity test on the DVOM, find the spade connector that is the common ground by touching one DVOM lead to the metal that would contact the base of the bulb, and touch the other lead to each spade connector. When you get continuity, that is going to be the brown wire.
2. Using the continuity test on the DVOM, touch the center contact on the backup light with one lead of the DVOM, and touch the other to the spade connectors until you get continuity. That will be the backup light connector.
3. Using the continuity test on the DVOM, touch the center contact on the turn signal light with one lead of the DVOM, and touch the other to the spade connectors until you get continuity. That will be the turn signal light connector.
4. Using the continuity test on the DVOM, touch the center contact on the small light on the side, and then touch one of the two contacts in the tail/brake light. Make note of which contact it is. Now touch the spade connectors until you get continuity. That will be the tail light connector.
5. Using the continuity test on the DVOM, touch the other contact from the one you made note of in the last step, and touch the spade connectors until you get continuity. That will be the brake light connector.
6. Match the labeled wires to the spade connectors on the tail light housings.
7. Leave the bulbs out and repeat for the other side. The reason for leaving the bulbs out is so you don't inadvertently get continuity through the bulb on the other side.
8. Put the bulbs in and test each light. IIRC, the outside two light bulbs are connected to the park light circuit, and will always light with the park lights.
9. Install the lenses.
10. Sit back, and enjoy an adult beverage.
I would have said a "frosty adult beverage" but I realize that you are in the UK, and Lucas sells refrigerators there.
I hope that helps you with your light issues.
Clay.