Is It Possible To Eat Healthy Food On A Very Tight Budget?

Healthy food need not be expensive.  It really can be done on a shoestring!  First of all you can cut down on meat consumption, particularly red meat.  Instead use lentils or chickpeas as the basis for stews or casseroles.  They are very cheap but also very nutritious and their fat content is much lower than meat.  In addition, they are full of fibre, something which meat does not have at all.
When cooking it may be worthwhile cooking large quantities and then freezing some of the food, so you have your own frozen 'ready meals' at a fraction of the cost of pre-packaged supermarket meals.
Always look for vegetables which are in season, which will be cheaper.  If you can then shop locally for produce and buy vegetables which are near their sell-by date, which can be used immediately but will cost less.
Finally try to increase the amount of pasta or potatoes in meals.  Baked potatoes are filling and low in fat but high in fibre and cheap to make.  But have fun trying to eat healthily within a budget and view it as a challenge, rather than a chore.