Wiring 1960s Desk Lamp: 2x15W Fluorescent Tubes, Dual Ballasts, Won't Start

Hi all,
I'm trying to fix up and restore a beautiful 1960s desk lamp fitted with 2x 15W fluorescent tubes for my desk. The tubes are new, the starters (4-65W) are new, the connections and continuity  checked but it won't fire up.
The engineer in me would love to convert it to LED, or even electronic ballast, but it's practically antique so I'd like to keep it original.
The lamps are connected in series, each with its starter, and are connected to the two ballast chokes, one on neutral and one on phase. The chokes check out at 22 ohms each, which seems about right, though I can't measure the inductance. They are transmitting the 240V voltage to the lamp circuitry fine.
Circuit diagram here (except the one in the diagram only has a ballast on the phase wire, while mine has one on each wire): https://www.wazipoint.com/2018/11/Tube-Light-Wiring-Diagram-with-Capacitor.html

Conventional wisdom would say that if the tubes and starters are new, the problem is likely to be the chokes, but as I say they seem ok, at least on DC resistance.
Any ideas gratefully received.

Many thanksPeter

Peter this rings a vague bell with me somewhere, I used to deal with stuff like this..  As you say the tubes are in series I think they would need 110V starters and you may have 240V starters.  Worth a check.If you can't get 110V starters you could try putting one 240V starter across both tubes, but I'm not sure this would work.

David, thank you for the reply, well remembered,you are a genius.
After you had planted the seed, I researched 110V starters and found there is such a thing as a series starter 110V 4-22W available here in the UK. It seems it was often used in small twin-tube luminaires. Hopped on my bike and bought 2 at 40p each and Bingo! All good now. They don't even stutter on startup but are instant-on like electronic control.
Thanks so much!
Peter

Peter...not so much a genius...but glad my ageing memory can still dredge up stuff like this.  I had an almost identical problem once, an old 2 x 20W light fitting where the tubes were wired in series.  Same problem, all checked out but no light.  It was only when I checked an old (faulty) starter that I stumbled on the problem.Always a pleasure to help, and thanks for the thanks, makes it worthwhile.

What's the first thing anyone does when they buy a 60-year-old fluorescent lamp? Yes, of course, chuck out the tubes (which probably have brown ends and a CRI of about 50) and the starters, which have also turned brown, and rattle. In my case, the starters were illegible and brown, and rattled when shaken, and there was only one tube.I was wondering about the point of the series wiring, and it occurred to me that by doing that you save one choke. All that copper and laminated iron you don't have to pay for.I can't believe how thick I was not to have at least suspected that 240V starters wouldn't heat up enough with 110V to close the bimetal switch. Duh. And no, a single 240 across both tubes wouldn't work as you need ionisation at both ends of both tubes for them to start.I'm usually a good boy on forums, but I'm a bit disappointed by the number of people (not here, I've just joined)who accept help, links, uploads etc and I never hear from them again. It sometimes make me just want to write again and tell them to stuff it.In my day, we were taught good manners, common courtesy etc etc. Grumble, grumble.
Peter

Peter if it is any consolation I had never even heard of 110V starters until I had that problem...Thanks again / David