First... find another garage. White smoke and low compression are NOT symptoms of a bent connecting rod. Also, you CANNOT inspect the connecting rods by removing the head - they're on the opposite (bottom) ends of the pistons.
White smoke and low compression are both symptoms of a blown head gasket. That's very classic. It doesn't sound like it's very bad, just beginning... but it CANNOT get better, and it WILL get worse in a hurry.
Consequences? A head gasket replacement is a relatively cheap repair; it should NOT cost you anything like a thousand pounds (that's nearly $2000 to Americans). Ridiculous! But... if you let it go until it gets REALLY bad (it won't take long to do that), then it could easily make the engine unrebuildable and destroy your radiator in the bargain. Coolant will be getting into your motor oil and wrecking its lubricity (besides turning it acidic), and the ruined motor oil will result in catastrophic engine failure. Meanwhile, high-pressure exhaust gases may be exchanging, getting into your coolant, and can very easily destroy the radiator (which is only ever intended to tolerate about 15psi of pressure).
Please - go find a better shop and let them do the work.