Tesco Car Insurance (and most likely their other financial products) operate a commercial email system which is populated by anyone who submits their address to them as part of searching for a car insurance quote.
That's not particularly unusual. Each mail that Tesco sends includes unsubscribe instructions - standard industry practise. However Tesco's instructions do not work. I have followed them at least three times since January this year to no avail. Despite this I have continued to receive unsolicitied commercial email (spam) from Tesco.
Tesco do not answer mail to their postmaster or abuse addresses, and do not accept mail for those local parts at many of their domains (they use more than one domain for their business: tescofinance.com, tesco.com, tescocompare.com, contact.tescocompare.com, tescoinsurance.com).
I would advise that nobody ever submit their details to a Tesco-affiliated company for these reasons. I have given up and blacklisted them on the mail servers which I control.
Based on the unrelated experiences of a friend of mine, I would have strong reservations regarding the quality of the services they offer, too - in particular their home insurance products.