Vibration that comes in around 50mph, peaks at 60-65, then fades is a textbook wheel balance issue — usually a thrown wheel weight or a buckled alloy after a pothole. If it shakes through the seat as well as the wheel, suspect a rear wheel or a worn hub bearing.
Common one this — especially in Scotland after a winter of frost-heaved tarmac and surprise potholes.
How to narrow it down yourself
If it's through the steering wheel only, it's a front wheel. Through the seat or the whole car, it's a rear. If it gets worse under braking, that's a warped front brake disc, not a balance issue. If it's there at all speeds and gets worse over bumps, you're looking at a worn hub bearing or a damaged tyre.
The four likely causes
1) A wheel weight has fallen off — happens all the time, especially on alloys. A re-balance fixes it (£10 a wheel). 2) A buckled rim from hitting a pothole — visible if you look closely, often the inside of the rim. Repairable from £40 or replaceable. 3) A tyre with an internal belt slip — the tyre will look fine but feels lumpy if you spin it by hand. Bin it. 4) Worn front hub bearing — usually has a hum that changes with cornering.
Why the cheap fix isn't always the answer
Plenty of places will just re-balance and send you away. If the rim is buckled or the tyre is faulty, you'll be back in a week. A proper diagnosis includes spinning each wheel off the ground to feel for runout and checking the tyres for visible bulges on the inside sidewall.
Realistic costs
Re-balance all four: £40–£60. Buckled alloy repair: £40–£90 a wheel. New tyre: £70–£200 depending on size. Front hub bearing fitted: £180–£350. If it turns out to be brake discs (warped, only felt under braking), front discs and pads is usually £180–£350 fitted.
Could it be tracking or alignment? — Bad alignment makes the steering pull or eats tyres unevenly — it doesn't usually cause a vibration on its own. If you've got a vibration AND uneven tyre wear, get both done.
Why does the shake only happen between 55 and 65 mph? — That's the classic balance-issue rev range — the imbalance resonates with the suspension at that speed. Below 50 it's too slow to feel; above 70 the wheel spins past the resonant frequency. Almost diagnostic.
Is it safe to drive on the motorway with it shaking? — Short answer: short journey at moderate speed, fine. Long motorway runs, no — vibration kills wheel bearings, tyres and your steering rack. Sort it within a couple of weeks.