Showhomes are usually owned and managed by the companies responsible for building and developing the estates on which they stand. Only the very largest companies are likely to directly employ interior design staff. The largest housebuilder in the UK is Persimmon:
http://www.persimmonhomes.com/
Other large house builders include Wimpey and Barratt:
http://www.georgewimpey.co.uk/
http://www.barratthomes.co.uk/
It might be worth contacting those companies to see if they have any suitable career openings but it's possible that they might follow the practice of smaller housing developers and engage the services of independent interior design firms. To get a foothold in one of those companies, you would normally require a university degree (or HND) in Interior Design (or in a related subject):
http://www.learndirect-advice.co.uk/helpwithyo urcareer/jobprofiles/profiles/profile528/
Chris