I am from the UK too so you are making it easy for me! What does your GP have to say about your skin issues?
First official recommendation is eat the right amount to be a healthy weight! I am a small build too as are some of my clients, but you still should have a Body Mass Index of 20-25 (Google for a BMI calculator) OR if you prefer a body fat percentage of 20%+ as you exercise regularly. The older we are the more weight/ bodyfat is recommended, only a modest amount every few years. If you weigh too little or your body fat is too low this stresses the body out just as being overweight does. Your body will preserve the fat it has in case you fall pregnant or there is a famine (evolution has not caught up with modern life!) so it will starve your skin and hormones, if this carries on long term your fertility and bone density *may* be affected. Be aware that those who exercise regularly do not just need more calories than average but they need more of every nutrient, this can be double for someone training five times a week!!
Healthy eating ... Omega-3 is a big one because it is critical to the health of every cell in the body; guidelines are at least three portions of oily fish a week but obviously as a vegetarian you cannot do that. DHA and EPA are the two long chain omega-3s that are essential for humans and they will be labelled on any fish oil or marine algae supplement. Seed oils supply only short chain omega-3s which are healthy but not essential: these are converted to the useable long form at a rate of ~10%. Basically you need MASSIVE doses of raw seed oils to hit 2-3g EPA and DHA. Therefore vegetarians and vegans should take a marine algae supplement - these are available from health food stores, Amazon or eBay. No special brand, just look for the DHA and EPA essential fatty acid content. It is safe to go higher than 3g and you may wish to do so if you think you may be deficient. On top of omega-3s we need other healthy fats: as a vegetarian you may well already be meeting the target of 70g+ per day (female who is not dieting) from nuts, seeds, avocados, coconut and olive oil.
Fruit and veggies: UK recommendations are for a minimum of five 80g portions a day BUT the research actually supports nine portions. This should be from the full rainbow of colours - red , green, yellow, orange and purple/ black and can include beans/ lentils. Again you may well already be hitting this target. Don't get stuck in a rut, eat a wide selection over the course of a week.
Protein: recommendations are to choose reduced fat animal products and to limit portions of meat, both of which are not an issue for you! One of the biggest mistakes my female and my vegetarian clients make is not eating enough protein early in the day, our bodies cannot store spare so ideally we would eat some every three to four hours, especially if we are exercising regularly. If you like maths you are aiming for 1.5g-2g of pure protein per day per kilo of bodyweight and this helps to repair every cell in the body including the skin. Beans, lentils, eggs and soft cheese are super healthy but they contain half the protein of meat and fish - so you need to combine with another protein source or eat larger portions - hard cheese and nuts are much higher in protein. Whey (milk protein) powder is another good option for those who exercise; it should not replace real food, but is ideal if you cannot eat before or after a workout and can be added to fruit smoothies or vegetable soups to round a meal out. Makes a rubbish tasting shake unless you mix with powdered milk! Dairy: UK recommendations are at least three portions a day - a portion is 200ml milk OR 30g hard cheese OR 150g yoghurt/ cottage I think. Again you could well hit this target.
Carbohydrates: UK guidelines are a minimum of half of all grains to be wholegrains, for your skin this should be all of them and preferably all low glycaemic index (keeps blood sugar stable). Low GI carbs include sweet potatoes, boiled new potatoes with skins, most fruit and veg, beans and lentils, barley, jumbo/ steel cut (not porridge) oats, wholemeal pitta bread, granary stoneground bread, brown pasta and brown basmati rice. You may already know these supply minerals which are just as important as vitamins and of course fibre. You will need larger portions or to eat more frequently if you exercise regularly, always eat an hour before a workout and again within twenty minutes of finishing (enzymes that repair, regenerate and refuel are most active). Whenever blood sugar drops too low the body releases stress hormones, which can contribute to various health problems, including skin complaints.
Fatty and sugary junk food should be no more than 10% of daily calories. IMO this is a toughie because a cereal bar or packet of crisps can easily swallow this up. Bad news is that I count *some* vegetarian convenience foods/ meat replacements as junk, great if has a high pulse or nut content not so if the recipe is bulked out with breadcrumbs because it will be low in protein and high in empty calories. You may be wise to this supermarket scam already but, if not, Quorn is a better bet than most. Note that the sugar naturally found in milk officially do not count towards sugary foods and fruit is a grey area (it's healthy so don't count it). As long as my clients are not overweight I don't count the sugar or fats in small portions of good quality 70%+ cocoa dark chocolate either because it's full of antioxidants!!
I am sure you are closer to a balanced diet than the average Brit, but hopefully something in this essay will give you a :eureka: moment. I will respond to the collagen topicals question at a later stage if necessary, Sarah is more experienced than I so I think it best she responds when she has seen your photos.