Aren't badgers a protected species in the UK? If they are you should know the law and regulations as you get answers to make sure that you are compliant with any steps you may take to alleviate your predicament.

Badgers are very difficult to eradicate once you get them and are a protected species in the UK. This will limit your options. They are omnivores and very determined, especially in the Spring when raising the little ones. Keep your compost bin sealed, don't put food out for the birds, fence in the vegetable plot. Rags soaked in Citronella will help deter but it's not a permanent fix. They need to be trapped and relocated.

A longstanding member here soaked old rags in Jeyes Fluid and draped them round her garden's boundary - she reported back that it did seem to deter them from coming into the garden, though they needed 'refreshing' with Jeyes fluid periodically and certainly after rain, but if your garden is very small, the rags won't look very attractive.

Just checked the UK regulations Bath. Capturing a Badger is an offense with a penalty of six months in jail or an unlimited fine. You can't even upset their burrows so to do anything with regards to them you have to apply for a license. Alot of tough stuff goes along with anything that has to do with them.

Would have to be done by a licensed professional.

There's no question of getting any kind of pest control, catching them or killing them - the only thing you can try is something to keep them out of the garden. Hence the Jeyes fluid on rags, they don't like the smell - that particular member had lots of badgers invading her garden too.

They are creatures of habit and follow scent trails and regular paths. So you need to find where they are getting into the garden and block it off. We have had to put about 100 metres of chicken wire round the garden perimeter. I know they can and will chew through it and dig under it. Here they cannot as there is the remains of wall all round us. To stop them approaching the fence we were told to put half filled clear plastic bottles as they are supposed to frighten the badgers away. It looks a bit odd, but so far no attempt has been made to damage the fence. The fencing is also loose which makes climbing it very difficult. I did hang Jeye's Fluid soaked cloths in the places where they had been coming in under the original fencing. BUT, since they have not been back so far this winter or spring I have not replaced them.
If you look on the Interweb things there is a lot of advice, but do take care, a lot of the things proposed are illegal (including the Jeye's Fluid thing).

Jeyes fluid is not illegal in the UK so long as you're not using it on soil (as people used to) - its still sold and its primary use is for sterilising pots, garden equipment, staging in greenhouses, that sort of thing. Soaking a few rags and hanging them from fences and the like within in your own property and garden is perfectly legal.

...and when it rains it all washes out of the rags, and down into the soil to contaminate the ground and ruin your entire vegetable crop. Then the badgers will look elsewhere.

Regardless, its not illegal; the fractional amount that might end up in soil as a result of excessive rain isn't an issue. And ultimately, there is nothing else to try that might work; its up to the asker whether they try it or not.

There is no chemical that can legally be used as a badger deterrent. Using one means you are at risk of committing an offence under pesticide regulations or wildlife protection laws.
Quote from Scottish Badgers.

It has come to our attention that some people may be using Jeyes Fluid, a strong smelling concentrated disinfectant, to try to deter badgers from using their setts or entering gardens. We would draw your attention to the fact that this is illegal particularly if placed in or near the entrance to a sett. It would amount to ‘obstruction’ of the sett - an offence under section 3 of the Protection Of Badgers Act 1992 as amended. In addition the chemical composition of Jeyes Fluid means it is toxic if ingested, and it can be lethal to some species. Any animal coming into contact with the chemical and then grooming itself could well ingest the chemical. This is a clear contravention of the Wildlife and Countryside Act 1981 Section 11 (2)(a). Anyone using or storing this chemical outwith the specified conditions is at risk of prosecution should harm occur to wildlife, pet animals, or humans.

Isn't it odd that badgers are protected and yet in some counties they are being culled....

Thankfully I don't have badgers near me. They are common in the prairies, central & western US, and Canada. But I got possums. They also like to dig around.

They have visited my garden now and then over the years. Their growls in the dead of night sounds like the devil is coming to get you.

Well, I've ventured out into the garden at night a few times only to be stared down by a gang of possums not willing to move.