Have you electrically tested either of the switches? It's easy enough to determine whether they are working.

 

I replaced a failed reversing switch (I can't remember if it failed off or on) with a new one and the new one didn't work.
The new switch tested out OK with a multimeter when I manually depressed the t*t so it was a question of tolerancing.
I spaced the new switch out from the gearbox with a washer under the ring nut and all was OK.
I can't remember whether the new switch was apparently stuck on or off, I'd imagine if I used a spacer washer to fix it it would have been stuck off (open circuit) at first, so this may not be your problem, but as rqt says, the first step is to test the switch actually works.

 

This was a common problem on the F the switch nut used to come loose and the brake lights were on and off as the pedal vibrated. As said here a few washers and tighten up the switch. You have to lie on your back on the floor to see what your doin.

 

Thanks for the reply's, I'm not great with electrical problems but I have checked the connections, as I changed the switch, I might get an electrician to take a look, the car is great, I have spent a large amount recently the get the engine upgraded to the N series spec with Payen multi layer head gasket, high tensile steel head bolts and a the updated oil rail. Took it to Scotland and did 1200 miles, and various shows, six months on its running perfectly, its just this reversing switch that will make thing great. payed peanuts for the car and its been far better than I would have thought.

 

Lovely car love the Blue. I don't know so what the problem could be might be a crossed wire in the rear light clusters. Your so lucky you can pick up these cars in UK for a song. They could be looking for 4 -5 grand for her here. I was looking at an LE with Trophy Cars Ltd. and although reasonable the VRT would be punishing to bring one in. On top of that the emissions on these is off the wall and the road tax is € 750.00 here. My 1800i here is € 636.00 which is mad anyway

 

Not sure to be honest, I don't think the reversing lights would work with a crossed connection.

The emissions are a bit high with these, its not cheap to tax here, but nothing like Ireland. The colour is what drew me to the car in the first place, I think its the Royal Blue is the best colour for these, it makes the car for me.

 

An entire multi page article in the latest Owners Club magazine is devoted to reversing light switches. Sad, but true, and may be helpful to you.

 

If your not a member of the MGOC you wont have seen the article.
Sadly the articles conclusion seemed to be its pot luck with no clear recommendation.
One thing that comes out is the plunger on the switch is depressed to operate the lights, so if the switch is screwed in too far the lights will be on all the time (your prob) and needs packing out.
The answer might be to remove the switch and then plug the wires back in, turn the ignition on to see if the lights are on or off, if on the switch is duff, if off the switch works and you can confirm this by pressing the plunger manually to put the lights on.
Then you can try packing it out with washers until it operates only when reverse is engaged, washers are cheap electricians aren't.

 

I'd agree with Deepfat I had a problem after putting a replacement gearbox in and finding the reversing light on all the time. The action of the switch worked perfectly when I operated it out of the gearbox, so I just packed it out with a fibre washer. It was interesting to read the article in Enjoying MG ref : reversing light switch, I'd say if you can establish the switch is working out of the box, engage reverse gear with ignition on and back it off till lights go out, pack out the difference and all should be well.

 

I fitted a new clutch mater cylinder today and changed the rubbers in the slave cylinder, while the cover was off I took the revers switch out and added a fibber washer, all working as it should now, thanks for the advice it was spot on, now I have to adjust my head lights. one is all over the place, I have tried to adjust it previously without success, I'm going to remove the bulb and re-fit it then adjust the light, fingers crossed.
Other than that the car is great, I bought this in 2017 for £650, and spent quite a bit getting the engine upgraded to N series spec, the full hit Oil rail, high tensile head bolts and a Payen multi layer head gasket, the cylinders were checked for level and found to be all correct. The head gasket wasn't gone but I wanted to make sure it was reliable.

Got to say I have been surprised how good the car has been, not had any real problems just the usual maintenance you get with any car, did 1200 miles around Scotland and back to Wales in all sorts of weather, went great all the time.