To get ranking in a short period of time, you can go with this idea: create a new landing page for the location “Bromsgrove” and optimize it well. Also, do local SEO, like local business listings so that local citizens of Bromsgrove can get to know about your website. Submit your online business into local directories, target local audience, understand their requirements and try to meet them!
You’ll have to create an inner page and rank it. Send all relevant links to that page treating it as a brand new site. So your inner page will have a url along these lines: yourwebsite.com/bromsgrove-mortgage-adive.
No need to create a new website, just a new page or a post with exactly the same title and wordings or one that contain the keywords you want to optimized. my 2 cents! I think gt3guy said it technically.
I agree that you do not need to create new website. Just create another page specifically for that location and do some local directory submissions and backlink activity for that particular page URL. This will help you rank for that particular location.
For the two different keywords, I suggest making a new page with exactly the same URL, related title and description with it, which contain the keywords that you want to optimize.