What Google search terms do you really need to focus your AdWords attention on? I’d suggest that they meet three criteria: they’re important to you; they get searched-for a lot; and you don’t have a great natural search position for them. Tracking down these terms is a really good exercise.
My favourite tool here is Google Search Console. In its “Search Analytics” section, you’ll find the searches where your site has been appearing over the last 90 days, or the top 999 of them anyway. We can use this list to identify the searches which meet the three criteria above.
Make sure ‘Impressions’, ‘CTR’ and ‘Position’ are all ticked, and set the filters to the UK and 90 days. Download the list to a spreadsheet.
Now, filter out any terms which didn’t get that many searches (say 50 or fewer), and any where you averaged being in the first few positions (say 4 or higher). Go through what’s left and delete the ones which aren’t very important to you. What’s left is a good list on which to focus your AdWords efforts.
Note that your starting list was the Google searches where you appeared in the results. If you didn’t appear at all, the term won’t have been in the list*. But if you didn’t appear at all and you’re sure the search is a commonly-made one, then you have an SEO problem. Google clearly doesn’t consider your site to be relevant for that term, and although you can compensate with AdWords, it’ll be expensive, as your low relevance will give you a low Quality Score. Prioritise SEO for this term, and get yourself in the results.
* As a separate exercise, it’s worth checking the initial downloaded list above against what you consider to be your priority search terms, to see if they appear at all. If not, is it because your site isn’t performing, or because they’re just not searched for?