'Black Tie Optional' and You're the Only Guest Who Isn't Rich
Black tie optional is a hedge in one direction. If underdressing is the more visible mistake, that decides how a small budget gets split.

It's a hedge, and only in one direction
Black tie optional, in small italics at the bottom of a thick card that's been on your fridge for three weeks.
The couple want a formal evening. They want the photographs to look like one. But they have guests who don't own a dinner jacket and don't want to buy one, and putting black tie on the card without the softener would either force those people into an expense or keep them at home. So optional gets added. What it means in practice: dress up properly, and we won't say anything if you can't manage the full version.
By convention the range it opens up is fairly narrow. A dinner jacket if you have one, a dark suit and tie if you don't. Floor-length, or a formal dress that reads as evening rather than as daytime. That's roughly it. Etiquette guides differ at the edges and none of it is enforced by anyone, but that's the shape of what the hosts are asking for.
What it doesn't mean is wear whatever you like. Nobody puts an italic instruction on a card to communicate indifference.
Which way to err, and why I can't prove it
In a room where the dress code has been softened, guests scatter across the range. Some go full black tie, some land in the middle, a few land low.
I can't point you at research measuring what happens next, so take this as a judgement rather than a fact: it's the person below the line who tends to stay noticeable, and the people at or above the middle who blend into the general impression of a formal room. Not laughed at — nobody is going to say anything, these are usually kind people — but findable across a room, and obvious in the photographs later.
If that's right, the two mistakes don't cost the same, and the strategy with £120 isn't to hedge toward the middle in case you overdo it. Aim high and simple.
There's a checkable version of the same advice, if you'd rather not rely on my read of a room. Hosts who write optional are signalling a formal evening and then apologising for the cost of it. Match the signal, not the apology.
£120, and most of it isn't the dress
The instinct is to put the whole lot into one garment. Split it instead.
Reserve some of it for alterations before you buy anything. A hem is one of the cheaper alterations you can pay for, and length is one of the most common reasons an inexpensive dress reads as inexpensive — it either puddles on the floor or hovers awkwardly above the shoe. A £40 dress hemmed to your height with your shoes on beats an £80 dress that's nearly the right length. Take the shoes to the fitting. This one thing does more than any other pound you spend, and if you want a second opinion on whether a specific dress is worth the alteration money, TrueTalk has an AI persona called Fashion Designer Sophia listed under fashion design, style consulting and trend forecasting — it can't see the dress on you or judge the fit, it hasn't been to the wedding, and the first conversation is free.
Buy fabric, not detail. With a small budget the failure mode is high-shine cheap satin. It flares under a photographer's flash and creases across the lap the second you sit down. Matte fabrics with weight to them — anything that hangs and moves rather than sitting stiffly away from the body — hold up better under evening light. Plain and dark is the safest thing in the room.
Then a small amount on one finished detail. Shoes you can stand in for six hours, or a proper clutch instead of your everyday bag. Pick one. Not both, and not a third.
Buy nothing that needs constant adjusting. A hem sitting wrong, straps that won't stay, an evening spent tugging at a neckline — the fidgeting is what people read, more than the garment.
Rental: a better dress, two limits
Rental gets recommended constantly and it can genuinely put a much nicer dress on you for the money.
Stock in your size on a specific date is a lottery and the popular pieces go early, so it only works if you're starting weeks out, not days. And rental terms won't let you alter it, which loops straight back to the length problem. If you're a height that off-the-peg evening wear fits without adjustment, rental is probably your best value here. If you're not, an owned dress you can hem may beat a borrowed one you can't.
The part that isn't about clothes
Worth saying plainly, because it's the real content of the question: the fear of walking into a room where you don't belong to the group is not solved by an outfit. It's reduced. A dress you're confident about removes one specific thing you'd otherwise be managing all evening, which is worth a lot. It does nothing about the conversation over dinner, or being asked what you do, or knowing nobody.
What helps there is duller. Arrive with the person who invited you if you can. Have a plan for the first ten minutes. Expect to feel it hardest at the door, and know that the acute version of it reliably drops once you're actually inside a conversation with somebody.
And you may be overestimating the room. Some of these weddings are full of people performing an ease they don't feel either, and at plenty of them nobody is doing any assessing at all.
Dark, long, matte, hemmed to your shoes
One good detail. Nothing you have to hold up.
That's a correct answer at black tie optional, and it costs about what you have.
