It depends on how good you want the finish to be - both aesthetically and in terms of protection against further rust.
The best way to do it would be strip the area of all loose paint, remove all rust with coarse wire wool, apply rust-converter, then etch-primer, then red-oxide primer, then normal primer, 2-pack acrylic colour to match your frame (or do the whole frame because you'll likely not find a match) and clearcoat (wetsanding between each layer) before a final cut-and-polish. Unless you already have the materials and paint laying around, this'll probably be more expensive than a cheap stove-enamel or powdercoat, and it'll take a lot of time and practise. It's possible to get a professional-quality finish with rattlecans, but you need to do a hell of a lot of wetsanding, and it'll be fragile. I wouldn't recommend using rattlecans (even Hammerite!) for that reason - if you try to do it on the cheap, it'll look crap and fall off; if you do it properly it'll look great but still be fragile.
Getting a cheap stove-enamel or powdercoat would cost £40-80 including sandblasting, and it'll remove all rust and you'll have a reasonably attractive finish. This is probably the best compromise between money/time/quality.
The cheapy option (but not necessarily the worst, depending on how much effort you put in) is to use some sort of direct-to-rust paint. Hammerite is an option, but it's not as tough or rustproof as it used to be. Professional products like POR-15 or Rustoleum are far better (I've used both for classic car/motorcycle parts, POR-15 is super-tough and Rustoleum comes in loads of colours - both can be difficult to find, though. Google 'Rustoleum paint job' to see how good it is!). You can remove the rust with coarse wire wool, apply a few coats of thinned paint (preferably with a high-density foam roller rather than a brush, as it gives a smoother finish), then leave for a week until it's really hard. It'll look okay, from a distance. If you want, after a couple of weeks of curing time, you can wetsand it with progressively fine sandpaper (say 600 to 2500) and polish it (T-Cut works tolerably well, everybody's dad has some in the garage) and it'll give as good a finish as a powdercoat (and just as tough).
The absolute cheapest option would be to simply give it a quick scrub with wire wool/a coarse kitchen scourer, and apply a few thin coats of linseed oil. It'll give you that rat look, and it dries to a hard finish and won't rub off on your clothes. You'll need to re-apply it every month or so, but it protects excellently against rust. You can pour it inside your frame tubes to protect against internal corrosion, too.
It depends on how good you want the finish to be - both aesthetically and in terms of protection against further rust.
The best way to do it would be strip the area of all loose paint, remove all rust with coarse wire wool, apply rust-converter, then etch-primer, then red-oxide primer, then normal primer, 2-pack acrylic colour to match your frame (or do the whole frame because you'll likely not find a match) and clearcoat (wetsanding between each layer) before a final cut-and-polish. Unless you already have the materials and paint laying around, this'll probably be more expensive than a cheap stove-enamel or powdercoat, and it'll take a lot of time and practise. It's possible to get a professional-quality finish with rattlecans, but you need to do a hell of a lot of wetsanding, and it'll be fragile. I wouldn't recommend using rattlecans (even Hammerite!) for that reason - if you try to do it on the cheap, it'll look crap and fall off; if you do it properly it'll look great but still be fragile.
Getting a cheap stove-enamel or powdercoat would cost £40-80 including sandblasting, and it'll remove all rust and you'll have a reasonably attractive finish. This is probably the best compromise between money/time/quality.
The cheapy option (but not necessarily the worst, depending on how much effort you put in) is to use some sort of direct-to-rust paint. Hammerite is an option, but it's not as tough or rustproof as it used to be. Professional products like POR-15 or Rustoleum are far better (I've used both for classic car/motorcycle parts, POR-15 is super-tough and Rustoleum comes in loads of colours - both can be difficult to find, though. Google 'Rustoleum paint job' to see how good it is!). You can remove the rust with coarse wire wool, apply a few coats of thinned paint (preferably with a high-density foam roller rather than a brush, as it gives a smoother finish), then leave for a week until it's really hard. It'll look okay, from a distance. If you want, after a couple of weeks of curing time, you can wetsand it with progressively fine sandpaper (say 600 to 2500) and polish it (T-Cut works tolerably well, everybody's dad has some in the garage) and it'll give as good a finish as a powdercoat (and just as tough).
The absolute cheapest option would be to simply give it a quick scrub with wire wool/a coarse kitchen scourer, and apply a few thin coats of linseed oil. It'll give you that rat look, and it dries to a hard finish and won't rub off on your clothes. You'll need to re-apply it every month or so, but it protects excellently against rust. You can pour it inside your frame tubes to protect against internal corrosion, too.