These days it's very unlikely that you'll find a third party only or third party fire & theft policy cheaper than fully comp. Seems the mere fact of asking makes it look like you're higher risk driving a banger that you don't care about.
I've tried upping the excess but the difference to the premium is never significant.
You might find the Omega cheaper to insure as a second car. Might even qualify for an agreed value classic car policy.
Add your wife, husband, sister or brother, any significant other, who is over 25 with a good record, as an additional driver if you haven't already.
Always shop around and don't leave it to the last minute.
Some insurers such as Direct Line and Aviva don't appear on comparison sites.
No insurer publishes all of the available policies online or on the comparison sites. Some policies are broker only.
So try a broker.
And remember you receive a no-claim discount, not a no-blame discount. A claim of any sort, even where all costs were recovered from the other party, will increase the underlying premium for the next 3 to 5 years.