As monte said a correction detail will make a HUGE difference. £300 is a lot of money though and theres smaller companies out there who are pretty good for a lot less money.
Failing that, try AutoGlym Super Resin Polish it has the red label and can be easily picked up from Halfrauds. It contains fillers which fill in the defects on the laquer to help reduce swirls and light scratches.
You will be very very lucky to find a detailer that will do a full correction detail for under £300
(Can take up to 3 days)
"This detail includes a paint correction treatment via an extensive machine polishing stage – swirls, holograms, micro-marring and scratches are removed, using the safest tools and techniques. This is a lot slower process as every defect that can be safely removed is so. Once corrected to the highest level the paintwork is then burnished to add a level of gloss and depth that is second to none. The results of this process can be breath taking and in many cases leaving the finish better than brand new vehicles in the showroom".
You can get great results by paying for a 1day detail (sometimes called an enhancement detail) cost about £150-£200.
This could be the detail that Lm-gauci is referring to.
"This is the most popular option as it includes a single-stage machine polish. It offers a first level removal of surface defects (oxidisation/swirls/holograms), leaving sharper reflections, added gloss and depth to the vehicle’s final finish. It is achieved by selecting a pad and product combination to suit the vehicle and its paint, which offers a level of correction whilst also offering a level of refinement at the same time ensuring a fresh defect free finish. This is where you start to see the benefits of a professional detail".