Hey,
My personal preference would have been to stick with the original URLs /locations/uxbridge and use the rest of the website and localised SEO to promote these locations pages and associate them with a particular service.
However, if your set on changing the URLs then take Joseph's advice and spend some time getting this right. As he says make sure that your redirects do not chain together and any previous URLs point directly to the new URL.
If you make sure that any changes are covered by suitable redirects then the negative effects to your site will be minimal in terms of links lost and if your research is thorough then you should put yourself in a situation where more traffic is available.
With regards to submitting a new sitemap to WMT - I would recommend this. Doing so will let Google know that you have made changes and prompt them to process your new URLs.
In the past I have uploaded the new sitemap as a brand new sitemap alongside the existing one - this allows them to continue seeing the redirected URLs and realise what they are doing. I'd then advise removing the original sitemap from WMT after around a week to two weeks.
This process has worked well for me in the past.
I hope this helps.