Hello
We're in West Hampstead, NW6 so not far away I would imagine. Whether to give vitamin supplements is really up to you. There are good reasons why you may want to do so living in fairly grey London without much sun.
Here's a quote from kellymom.com which has a few more links about vitamin supplements you may want to check out:
World Health Organization information states on the subject of vitamin D from the Sun, "Two hours is the required minimum weekly amount of sunlight for infants if only the face is exposed, or 30 minutes if the upper and lower extremities are exposed." This guideline is from a study [Specker 1985] of exclusively breastfed Caucasian infants under six months old at latitude 39°N (Cincinnati, Ohio, USA). Darker skinned infants may require a longer time outside (three to six times the sunlight exposure) to generate the same amount of vitamin D [Good Mojab 2002].
London is further North and apparently during October-April getting sufficient Vitamin D from Sun exposure is more of a problem but it's worth bearing in mind that apparently vitamin D is not 'best absorbed throught the digestional tract'.
In the diet, good sources of vitamin D are cod-liver oil; sardines; herring; salmon; tuna; milk and milk products (but cow's milk is relatively low compared to other milks);
Good sources of vitamin A: liver, fish-liver oil, carrots, green leafy vegetables, egg yolks, enriched margarine, milk products, yellow fruits.
The main reason I chose not was quite honestly Sam hated the supplements we started on and spat them out and got sad. We tried a couple and he's never been a fan of taking from a spoon or syringes. It seemed that if other people were choosing not to do it for other reasons there might be an alternative. I did my reading after that! We focus on diet and playing outside everyday even in Winter. I haven't exactly given you a definitive answer here but hopefully some stuff to consider.