Read this thread earlier but wanted to reflect on my initial reaction. And I am basing it around the fact that regardless of size, any firm that can have such a huge risk to carry should have checks and balances, and it seems your employer didn't.
To be honest, arguing whether it was or wasn't gross misconduct is a bit of "angels dancing on a pinhead" activity because at a very basic level it is possible that an employment tribunal would conclude it was a fair dismissal, even if not gross misconduct. I am not convinced they would find it fair - but equally I am not convince they wouldn't. ET's are always risky, and this one might carry more risk than usual because (a) the error you made was serious and (b) it's a small employer and therefore held to slightly lower expectations by ET's. It's not a place I would recommend anyone wanting to go to anyway, but avoiding an ET would be a good idea imo.
That said, I think they have behaved appallingly towards a single (albeit huge) mistake by a long-standing member of staff, so I don't have any compunction in saying that you should tie the bastards in knots!
So by all means appeal the dismissal, although I am not sure that is good advice. All trust and confidence in them has gone by now - how can you even think about going back to work there now? Plus, if they have put a foot wrong at this stage you are giving them a chance to bring you back, give you a final warning, then "sack you correctly" for any wild reason they can dream up.
What I would do is:
(a) Lodge a claim for early conciliation with the intent of taking them to tribunal
(b) Aiming to achieve a settlement agreement based on a mutually agreed termination (so neither dismissal nor resignation), and an agreed reference to that effect.
(c) If that doesn't work you lodge the tribunal claim and then it becomes a game of chicken - who blinks first. It will probably be them. You don't have to do anything and you don't need legal advice - they would be idiots not to get legal advice, at which point the best legal advice they can get is that continuing to fight this will cost them dearly even if they win. You, on the other hand, have nothing to lose! It may be a long game, but it can't make things any worse than they are now.
You made a mistake. Nobody is perfect. Their company isn't perfect if they have no checks and balances. At worst you are equally at fault. But I wouldn't take this lying down.