Hi MattJH and welcome!
Re: Question - can a scoot save my sanity?
Short answer - No! If you read the many posts on here you'll soon realise that some maxi-muppet members lost their sanity a long time ago, and others put the fun in dysfunctional.
However, if it
is too late to save your sanity - you'll be in good company.
There are many great recommendations already on this thread so to confuse you further I thought I throw this into the soup of decision!
Maxi-Scoots can be the easiest, cheapest, most convenient and most 'exciting' way to get from A to B. They generally offer better weather protection, a more relaxed riding position and better storage space. There's also the convenience of the automatic CVT - no gears or clutch - just twist and go. There's also less chance of you picking up the lurgy from fellow coughing and sneezing commuters. The flip side is that there's a higher chance of being hurt if you're involved in a RTC, so you'll need good kit.
If you're uber competitive then get the fastest production Scoot available - the Aprilia SRV850cc - but you'll need to stretch your budget to £5k! (44+MPG & 100+MPH)
If you're the competitive sort that loves to fettle and needs to be the first away from the lights then Tmax is the wee beasty for you. A lean, mean overtaking machine. (56+MPG 100+ MPH)
If you're still trying to convince your head and your heart that you're 'sensible', then the Burgman or Maxsym 400 is maybe the best of both worlds. Not quite as quick but nor as thirsty - and you won't be wondering why you spend so much on brake pads!

(70+MPG & 90+ MPH)
£3-£4k gives you a lot of choice in the second hand market, but don't forget nothing is set in stone. You could start off spending less, earning brownie points in the 'sensible' stakes (and losing less if it's not your cup of tea) and buying something else!
Here is a great website to see how you might 'fit' on the most popular motorbikes and Scoots:
http://cycle-ergo.com/" onclick="window.open(this.href);return false;
Fuelly is a great place to compare MPG's - but remember to change units to "UK" up in the top left:
http://www.fuelly.com/motorcycle/" onclick="window.open(this.href);return false;
Having done a quick search on Biketrader I came up with these in your 'area':
http://www.autotrader.co.uk/search/used ... pe/scooter" onclick="window.open(this.href);return false;
There is a £2,299 2010
400cc SUZUKI AN BURGMAN that's done 28895 miles pretty close to you that you might be able to haggle down to £2,000?
http://www.autotrader.co.uk/classified/ ... ?logcode=p" onclick="window.open(this.href);return false;
There's also a practically new 2012 MAXSYM 400i for £3195 that's only done 70 miles!
http://www.autotrader.co.uk/classified/ ... ?logcode=p" onclick="window.open(this.href);return false;
Both these bikes have fab reputations and ideally you gotta test ride both!
Happy hunting!
P.S. In MY experience on this forum 400cc riders are the most balanced individuals!

If you want to be incrementally better: Be competitive. If you want to be exponentially better: Be cooperative.