"I've looked at other campaigning groups' websites in eg London and wished we had something similar."
Whoever is responsible for decision making at Spokes needs to agree with you.
It may well be that some or all of them already do.
The second problem/opportunity is deciding on the various 'who is it aimed at', 'what should be on the front page', 'what should it look like' questions.
I understand about inertia and 'needing volunteers', but the latter is mostly an excuse.
At this stage it should be about considering the possibilities/options and making some decisions.
It's not about handing over control and waking up to find a whole new web site that may or may not be better.
All sorts of things can be tried online and viewed by a selected/restricted number of people.
Spokes has never been rich, but it is seldom destitute. Perhaps it's time to pay for a bit of advice? There are various organisations specialising in assisting Vol Orgs.
There has been some concern about 'losing the archive'. But that's not the way the web works. If you have "space" (basically very cheap) you can keep anything. In the past not everything survived a revamp or change of server, but that was presumably by choice.
If most of the concern is 'making the front page look more attractive to new people' then not a lot needs to change - though some new pages and thought about navigation would be wise.