Hello! That is a great news! :-) Congratulations! For one of my sites - there are 20 inner pages - Google keyword tool also shows no activity with these keywords, BUT - I do have phone calls for these areas and the prices for the job are nice. So there is no guarantee that if it shows nothing that there is no potential clients there! :-)
There are many factors with the SEO - first you must know the age of the site + repair something on the site itself to make it on page SEO 100% perfect. If it is built to rank for some areas - I would suggest putting Google Maps on the particular page - it really works for the ranking in Google + you can create a video for the client + post it on YouTube + use fiverr to get some likes, views and comments - it helps ranking again + put the embedded code on all pages. YouTube is Google property so when it crawls the pages - google loves videos as it owns YouTube :-)
Now about the link building... It is pretty risky whenever you are working with clients... I used to rank this site - http://skypaintingdecorating.co.uk/
on #1, #2 places in Google with SeNuke XCr, BUT then I wanted to try one private blog network - HUGE mistake! Everything went to oblivion - #500... So with the clients - more research is needed.
That is why I am creating inner pages (for the keyword and the area) + I am creating backlinks with DIFFERENT KEYWORDS every time. For example if I want to rank "carpet cleaners Chelsea" - the first campaign - 14 days is for the keywords: carpet cleaners Chelsea, Chelsea carpet cleaners, professional carpet cleaners Chelsea, expert Chelsea carpet washers, etc. - a lot, a lot of different LSI keywords - this is kind of a guarantee!
Also, social media backlinks are a great factor - you can order them from fiverr as well. Google now is doing another update (I am so tired of them!) and it really, really wants to get rid of the junk! So the link building most be done very carefully! And my opinion is: First - great on page optimized site + then steady linkbuilig. :-)
Also - if it is an UK site - then manual submission to .co.uk directories (local ones) will help a lot! Nowadays SEO is not easy - and more work is needed - the client must know that - otherwise there are a lot of Indian guys (nothing against them - only respect) who are providing cheap and "GREAT SEO" with a bunch of submissions, but after 2 weeks the site will be NO WHERE TO BE FOUND! :-)