Let me make sure I get this right.

You bought a new car (brand new?) c March 2018. First years tax was part of the deal. You thought there was a direct debit in place for subsequent years but for whatever reason there was not.

Somebody's fat finger meant the address on V5, and therefore that used to send postal reminder (V11?) was wrong. Right road but door number incorrect and that of an unoccupied property.

Consequently all correspondence, V11, chasers and subsequent court summons were sent to wrong address. As you had no knowledge you could not take action to pay nor to respond when court process was threatened. Only later, probably when enforcement got involved, did somebody take a positive step to trace you.

Is that accurate? Are the proceedings in Magistrates Court or County Court?

You didn't notice mistake on V5 nor fact that no DD was taken. We pay our car tax by monthly DD and get an annual e-mail from DVLA to confirm payment regime. Were a DD in place you'd have had that or paper equivalent. The DD, compared with say Council Tax, mortgage or gas/electric is a trifling amount. Somebody on a very tight budget or with sort of habit my late Father had for line by line analysis of bank statements might notice. Not sure I would.

My suggestion would be to approach the court, explain that the summons was not received due to being wrongly addressed and ask for judgement or conviction to be set aside. There will be forms to fill in, a sworn statement to be made and possibly a fee to pay.

If successful that would reset the clock on the court decision and costs. You could then ask prosecutor/claimant (is it DVLA, police or some other outfit?) to withdraw the summons on basis there was an error and, as tax is now paid, no loss to the public purse.

Should be OK without a lawyer. Be patient and don't take out frustration on court staff even if they're initially sceptical. You wouldn't believe how many people convicted of this sort of minor offence or who get a parking penalty enforced claim to know nothing until the bailiffs arrive.

Good luck and let us know what happens.

As ever your local Citizens Advice should be able to offer advice /support if you need it.

My thoughts would be that having paid, you should demand that EH recompense you since it was (presumably) their error which led to the situation, You need to get the V5 sorted out asap, and maybe EH can help here also.