Does Nigel let you touch his teeth, at all? I wouldn't use the instruments - trust me, they WON'T hold still and what'll happen is you'll nick the gums, they'll bleed, cry and freak out - so no tools.
Only a professional can remove plaque build up, we can't (it's like cement, very hard and stuck on there) - but to prevent FURTHER build up if you can touch his teeth, you can help a little bit.
Don't use a brush, not to start - use tooth cloths, they sell them. You can wrap them around your finger and rub your babies teeth. Fena has started to let me do this with her (only if I put a little liver paste on the cloth of course) - it'll wipe away any future build up.
Lucky, my youngest boy who died of cancer in 2016... he needed a dental but was dying of cancer. He got diagnosed but was still happy and healthy, eating, drinking, playing, no signs at all so we (vet and I) decided to wait until HE told me it was time.. it was a few months and during that, he could have used a dental but since he was dying, we didn't do it. So I used the cloths.
I DO NOT RECOMMEND THIS - in his last month, I would wet a cloth in 1 tsp whiskey and 1 drop clove oil then rub it on his teeth and gums. He'd let me, wasn't thrilled with it but wouldn't fight either. It kills germs and numbs, so he could eat his food. This was sign 1 though, that his time was coming.
At this point with Nigel I'd say a couple things.. if he'll let you rub his teeth, use the cloths. See if you can contact any animal charities, etc.who might be able to help you. Use your phone book, online.. call as many people as you need to, you might be able to find someone to help. Even call vets.
The worst that could happen is they say no but they MIGHT say yes so it's worth it.
Have you gotten an estimate on what his dental might cost, if you had it done...?