First British passport: “passport you used to come into the UK” issue

I’m looking ahead at the requirements to get a first British passport and I’m a bit worried by this:

You’ll need both:

- your naturalisation or registration certificate

- the passport you used to come into the UK or the foreign passport you’re included on

The thing is, I’m renewing my French passport, and the French consulate in London doesn’t give you back the old passport when they replace it, so I won’t have the “passport used to come into the UK” anymore. Is that a problem? Can I just provide the new one, or do I have to travel in and out of the UK with the new one first? Or something else?

Thanks

Not an issue.
You can’t provide what you haven’t got.
In my own case I just provided my current foreign passport and got issued with a British passport within 10 days. Later I saw this requirement, and I actually had that old passport.
Note you will be/are a BC and you can’t be refused a passport without good reason. HMPO just want to check that you don’t hold travel documents in different names.

I'd make a full colour copy of your old passport before you send it in for renewal, just in case.