I’m thinking of buying a 2009 model as above, only 34,000 on the clock. Good service record up to 2017, but it has not been serviced since Aug 2017 when it had done 30,000 miles. So only 4,000 miles driven since then, but almost 2 yrs gone. Should I insist on a service before I buy it?

If you insisted, they would more than likely change the oil and filter and stamp the book, but it's not really the oil that's likely to be an issue.

When you ask for a service, make sure you know what you'll be getting!

34,000 is pretty lightly used, it might be worth having the brakes checked for wear, it's more than likely they are still the original and could be on their last knocking.

I'd also say it would probably need the brake fluid and coolant replacing as well.

The rear axle needs a good check over as they are prone to rusting up badly, particularly around the lower spring seats.
If it looks rotten, walk away as a new one is big money.

While you're on your hands and knees, the engines sump can rust up as well leading to oil leaks.

Take an extended test drive, make sure you take it over some speed bumps.
The 1.1 have a wiring fault in the loom to the coils/injectors that can cause the car to cut out or stutter.
Most owners first notice this over speed bumps and humps, it is fixable but a bit of a ball ache.

Make sure the steering is smooth, it's electrically powered and most problems are due to low/old batteries, but they can suffer problems with the torque sensor.

If I liked it, I would try and negotiate some money off and go over it myself, I'd know it's right then.

Old father time is far more damaging than miles. It will need the following
Battery is likely to be toast. They do not like standing unused.
Full brake examination for pitted discs, leaking hydraulics and cracked hoses.

Brake fluid change.
Potential rusty bits (as above checked). Axle can be treated with a good anti corrosion spray followed by Waxoyl or similar.
Steel water pipe across front of engine is notorious for rust. If it leaks you will probably lose the head gasket.
Clutch should be ok but any hassle with clutch action probably the hydraulic master cylinder. Change the hydraulics as you cant get repair seals.
Cam belt will probably break. It wont hurt the engine but the car will have to be towed for a new one to be fitted

The engine will probably feel sluggish to drive and not especially good mpg. It will need a few hundred miles of fast motorway thrashing to free it up. I has this with a 900 Seicento. It free'd up nicely but at first I thought, how can Fiat think this is close to adequate?

I bought my latest Active Eco '60' Reg 2 years ago - with a full fiat service history up to 2016, 28k on the clock. The cam belt was replaced as part of the sale.

Echoing what others have said, or should that be Eco-ing what others have said - I had a full service at my local independent garage, fluids, plugs, filters, oil, antifreeze, brake fluid change and hand brake adjusted when the MOT was due last September. I also bought a new battery as I kept getting the power steering warning light on and alls been fine since.

The engine felt quite restricted and sluggish, but with regular use and the occasional Italian tune up on the A21 it's running much sweeter, free'er and happier. MPG improved quite a bit too. I'm now on 35k miles