I'm a trainee solicitor. You should threaten to report them to the Solicitors' Regulation Authority and/or the Solicitors' Disciplinary Tribunal for failure to comply with the Solicitors' Regulation Authority Code of Conduct, Rule 1.05 (Core Duty: provide a good standard of service to client); and Rule 2.04(1) (duty to provide client with information about cost at the outset and when appropriate). Google SRA Code, it's the first thing to come up.
When I looked this up, I expected to see a clear rule in the Code saying an invoice has to be sent within a reasonable time. The Code doesn't have this, but it does refer you to Law Society guidance which says invoices have to be sent within a reasonable period of time. My firm's internal guidance also says this. I've seen much larger amounts get written off when it's not been billed for a few months, so I'm very surprised they're chasing you for £100.
However, the fact is that I've no idea what would happen if it went to the SRA/SDT because the SRA Code doesn't have a clear rule on it. You'd be relying on a wider duty of good client service/reasonable conduct, which is much more wooly. To bill you a year late seems extraordinary though.
Also, the fact that they've taken a year to bill you indicates that they may not have proper accounting procedures. They might be in breach of the Solicitors' Accounts Rules. You might therefore threaten to blow the whistle on them to the SRA for this, too.
Also your letter of engagement from the firm should have a clause stating the basis on which you will be billed, how frequently bills will be issued, etc. (and I very much doubt it's "annually" – most firms say "regularly"). If your contract with the firm had no such clause, that in itself is likely to be a breach of the SRA Code.