Google only shows a few of the backlinks it knows about so it should about more.
Having a quick look through your site I would suggest adding some more content to your home page. This where your links are pointing to and is also considered to have more weight than any other page.
If you follow this link it will show what Google is reading from your home page,
cached text only
Notice that you only mention your keyword phrase three times on the page (not including your title). Try and write about 200 - 400 words focusing on your targeted keyword phrase. It will need to flow nicely and not seem like it has been keyword stuffed. break the content down into about three or four paragraghs using your keyword phrase as sub titles. Vary the sub titles slightly and use an H1 tag for the fist title and a couple H2 and H3 tags for the rest.
This will help Google to theme your site, something it has not yet managed to do,
similar pages search. This is basic on-page optimisation and should make off-page optimisation (link popularity) easier to conduct.
If you do a
allinanchor:"florist tunbridge wells" search on Google, your site is in P1 and would suggest that you have more links with "florist tunbridge wells" as anchors then any other site. This can mean one of two things.
1. You just need to focus on your on-page SEO
2. You have used the same anchor text for too many links and set off one of Googl's link filters. Meaning that the target page is being penalised.
With you only have a small number of links I would find it hard to beleive that it is number 2.
There is one more thing, how old is your site? You have no PR which would normaly mean your in the sandbox (because you have links so PR should be passed) and also how old are your links? Google sanboxes every new link it finds for some time and only when the link reaches a certian age does it pass on any influence. I would guess that your site is not ranking because of both of these reasons.
If it is the sanbox just do a bit of on-page SEO and wait it out

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Hope this helps.