In theory yes, but the results may not be great, I have done it in the past where all the lacquer was gone leaving no ridges and had success, even with rattle cans if you are diligent you can do a great job, I have sprayed virtually a whole car ( Honda CRX) with nothing but rattle cans and done that good a finish on it that my mate who is a paint sprayer by trade could hardly tell the difference, its all about preparation, then leaving the paint long enough to dry before trying to flat and buff it (weeks).
What you could do is get a can of clear lacquer and try it on a small panel, put enough coats on then leave it a good few days, flat it with 1000/ 1200 grade then t-cut/farecla or similar and then polish it and see how it looks, if its poor you would have to get it resprayed anyway so no big loss, but if you go about it methodically and keep everything spotless you may well be astonished at what can be done with just cans and for a fraction of what a company will charge!.
£3.5 k for a full respray on an Elan is excessive to say the least, I know 3 really good painters who know their stuff and would charge about a grand for a good paint job on an average sized car, or 400 if I prep it and buy the paint.
If you have to get it painted elsewhere, shop around, don't pay more than 2g for a full hit no matter who does it. HTH.
Jamie.