OP unless you're thinking about branching out into wearing more dresses, I personally wouldn't buy one just for this single occasion. I know you said wide leg trousers remind you of work but, given how you're spending the rest of the day, I think if it was me, I'd look for some in an un-officey colour (cos I'm into colour at the moment) and I'd team with an equally colourful, non toning, possibly clashy top.
For example, there's quite a lot of bright green around at the moment so I might look for green trews - I've seen some in Oliver Bonas and I think the Uniqlo C collection has some coming out. And then maybe something like this Oliver Bonas top
Or, if you've already got a nice top, then I might go £7 over budget for these Me and Em red trousers The size 12 has gone but I think they're normally generously sized so sizing down might be fine. I know some people will say you're mostly sitting down so your top half matters more but I find there's often quite a bit of promenading going on at dos like this.
I've been in the Savoy once, in the afternoon, just for coffee and cake, admittedly a few years ago, and most people I saw were dressed up, although not to wedding level. The hotel interior was fabulous, as was the service. Have a lovely time.