The tech industry doesn't feel particularly stuffy or formal - it would be different if you were a barrister.
I think your dress & boots or your skirt & blouse & boots will look fine.
Try putting the dress over the skirt for a statement look.
Get some quality opaque black tights with your £10.
Do you have necklace or earrings or belt to play with?
And if your boss comments on your outfit, suggest if they're doing well enough for a presence at the Savoy, it might be time for a raise...
To add to your wardrobe on a budget, I'd suggest:
Some plain silk, cotton or linen t shirts, black or your best colours, to go with the skirt (I have two linen v-necks from M&S that go with everything including my necklaces)
Yes, some smart black trousers - good under the dress and with the blouse and boots, so gives you more options.
Charity shops have yielded some great bits of distinctive jewellery for me.
Have a fun event 🤗