It depends on the provider, I would guess. I just ported my ISDN lines onto a Gamma SIP trunk. They require the caller ID you send outbound to be the national number, less the leading zero, so for the number 020 8880 xxxx on my office extension, edit the extension, click the Other tab and enter 208880xxxx in the Outbound Caller ID box.
In the Outbound parameters section of the VoIP provider, I had to make sure that the From field was corrrectly configured; I have mine set to "From: User Part" = "OutboundCallerID from Extension settings" and "From: Host Part" is set to "ContactUri"
Depending on what your provider wants, you may need to tweak differently.
Also, note that there's an 'Outbound caller ID' on the port screen for the provider; I left that blank.
I also had to prod the provider to authorise the caller IDs in their database, which they didn't do by default. But if it's been working with your old kit, that shouldn't be an issue.