Sounds like you have a very sensible GP.
The evidence for AD's is remarkably poor so correcting nutrient deficiencies is getting to the root of the problem. However other common nutrient deficiencies that are associated with depression are MAGNESIUM, Vitamin D3, zinc, and omega 3. Poor sleep doesn't help either and so MELATONIN may also help.
The magnesium, omega 3 and vitamin d3 are all anti inflammatory agents and these all work in the brain to reduce inflammation. (Not surprisingly many of the anti depressants also double as pain medication for their ability to reduce inflammation in the brain)
You can get a 25(OH)D test to check your vitamin D level from City Assays Blood Spot Test Kit Order Line Tel: +44 (0)121 507 4278 Monday - Friday 09.00 - 17.00 UK time
£25 or £20 if you have friends/relatives and bulk buy.
However if you haven't been supplementing with effective strength (5000iu) vitamin D3 over the winter then it's probably worth supplementing first and testing after 3months. Effective strength D3 is best sourced (cheapest) from IHERB/VITACOST or other US discount supplier although some of the amazon/ebay deals aren't too expensive.
Omega 3 probably requires over 1000mg of EPA + DHA daily to make much difference. Simply Supplements triple strength fish oil are probably the cheapest UK source particularly if you belong to the cashback site Quidco.
Magnesium is best sourced from an ALBION MINERAL CHELATE or you can use epsom salts or dead sea salts (magnesium sulphate or magnesium chloride) in your bathwater If you search this site for magnesium you'll find several other threads on which is the best source of magnesium. Obviously food sources are best but you still should more than meet the RDA and that can be difficult.
I think perhaps it's worth pointing out that correcting micro-nutrient deficiencies takes time and you cannot expect to feel better immediately. It took me several years to get my bipolar depression under control. allow 8~12 weeks to see any change from omega 3 vitamin D intakes and the benefits will go on incrementally for probably 2~3 years before your reserves are fully recharged.
The zinc is to improve melatonin production. (don't overdo the zinc)
Bright light exposure midday and subdued evening light and total darkness while you sleep also improve melatonin production. That also is best sourced from Time Release melatonin supplements from the USA (you can't buy it otc in UK)
I should perhaps have made the point that these suggestions are complementary to your doctors prescription and not instead of. These are the most common micro nutrient deficiencies that occur from modern diets and they all work together so the sum is greater than the parts.