Sound like you need to get married ASAP for emotional, legal and financial reasons and you'd like to do it in as romantic way as possible. This is entirely possible!
(1) I'd start by picking a date.
You want enough time to plan and enough time to be more settled hormonally. I'd make it well into summer so as to try and help ensure the sun will shine on you on the day (well, as much as we can guarantee sun in the UK).
(2) Next - your budget! Work out what you can possibly afford without putting yourselves in difficulties. Find out how much (if anything) a parent might contribute. If your parent(s) have always expected to help out with something towards your wedding - tell them the time has come 
(3) When you know your budget, work out what parts of your wedding you want to spend the most on - the dress? the party? the venue? and allocate money accordingly.
(4) Start looking around for stuff that fits the budget you worked out. For instance, if you put £100 for your dress, you start looking for dresses £100 and under. Do the same with it all - rings, venue, etc. Try not to let the spending spiral out of control which can be a temptation. You can get frugal websites for ideas on where to find dresses. You will be surprised at what can turn up when you are tuned into it.
I had an easy, cheap, quickly-arranged wedding. I come from a small scattered family and my husband and I are both shy and didn't want much of a fuss. I arranged it in 12 weeks and we spend under £1000 on the day. We could have spent less on our rings, but my dress was only £100 off Ebay!
Good luck - you can totally do this. It can even be fun. As a pp said, it can be better to have this type of wedding - think of the politics and years of stressful planning you won't have to go through. You are basically arranging a smallish fun party for people you love and you'll be getting married at it.
Good luck 