How about timber t&g?

I had not thought of either so thank you for this - I will look into what t&g is available locally, I have had some trees cut up and planked recently but I don't think the saw will cut very thin but I can get some nice wide boards out though.

Paper? would this be plain ordinary lining paper?

Wouldn't wood make it rather dark? I guess you could paint it.

Thanks ali I forgot to mention the Vapour barrier between battens and insulation which I would do also.

I would screw the battens with 100mm screws in line and below the existing rafters but pilot hole first to avoid splitting. I only use nails these days for fine finishing such as architrayves and t&g. Screws will pull the insulation nice and tight. Nails just bounce and may cause damage to original rafters if they hit a knot or are too close to the edge.

I fix a layer of polythene as well -I worry that tape can lose its adhesion over time. Cheap polythen cover sheeting is about £15 for 25m x 4m roll so its a no brainer. Just staple it to the insulation

never seen a batch of insulation batts delivered with foil coating intact on all the boards.
just realised we're commenting on the assumption that the rafters are running in plane. highly unlikely on a traditional barn, or any roof you've not done yourself come to think of it. solution to that is time consuming work with building strings that will pay dividends and more when you come to insulate, board, finish whatever. not so critical if lime plastering but always worth the time while the kettle boils standing back taking it all in and setting up some strings to give an idea on how the existing roof plane sits along the line of the rafters.
whats happening at the ridge line ? if you have raised collar ties you could spend half a day setting up your levels and plane, but the reward will be worth it in time saved when finishing.
of course you could use a laser line but strings allow the whole roof to be set-out. measure what you need to pack out to a common level, order 3x1, 4x1 accordingly and attach to the edge of the rafters and ties. Pilot hole first (even spend a few minutes with a chalk marking serious knots to avoid first- saves time later changing busted drillbits). (Mike, when u have a paslode - habit is to shoot nails : into anything that doesn't shoot back, usually).
was a suggestion on a thread before to loose fit insulation batts with wedges and fill with exp foam. maybe mikes tip. set batts up to the string level proud of the original rafters, allows you to fill the 2"void (width of rafter) between rafter and string line with more exp foam and prevent thermal bridging. before final overlayer of ins. batts measure from a fixed point the centres of the rafter add-ons and make a proper note of the fixing point locations using the dimensions.
a chalk line more than pays for itself on these jobs too.

actually why bother with polychemical stuff - why not use warmcel. not sure on what thickness you'd need for reg's compliance. i've only got 3" thick in between timber frame, roof and floor and dont need heating on after todays sunshine.
good luck

I never used tape (too expensive for a possible temporary job) I always used polythene as a combined air barrier/vapour control layer.

What about multilayering boards then there are lots of foil layers (vapour barriers) within the insulation both on the warm and cold sides.

I'm new to this forum and probably a bit late for the o/p's benefit. I have insulated a concrete ceiling in a top floor flat using Celotex with taped joins. To hide it and provide a good finish I used a Clipso stretch ceiling. Easy to fit and a beautiful appearance. Google Clipso for the manufacturer's website. There's a UK agent if you need to find out more - I'll give you details if you need them.