I grow lavendula angustifolia, the ordinary English lavender. I always cut mine back after they have finished flowering, but I never cut into old wood, just the new growth. I tend to replace them after about 5 years though, because eventually they completely lose their shape. I have read that they can withstand a hard cut back, but I am dubious about that. I am sure you will get more advice from others on the site.

I always cut back to about an inch above where the stems become bare. Like Melchise I don't cut into old ,leafless wood.

I have cut into old wood, where a bit has 'stuck out' and found that it will re-shoot, but I wouldnt do much at the time.

Would like to say thanks to you all. Will get stuck into it at the weekend.
Fagan.