Parent Free Life Cover - More than 1?

Unless the terms and conditions say that the policy is not valid if you have a similar policy from another provider, or you are asked to declare other policies before they will accept you, then you can have policies from as many different providers as you like (or can find).

There's no obvious reason why Post Office would care whether you also had a policy from L&G. As above, from their point of view the offer is a marketing gimmick. The cost of providing a few thousand pounds of life insurance, for 12 months, to someone of normal child-bearing age (so very unlikely to die imminently), is probably measured in pennies rather than pounds, and they're offering it to make you more aware of their brand and to sign you up to their marketing lists. From your point of view it's free, so no reason not to take it if you don't mind a bit of marketing bumph, but don't treat it as an alternative to a proper life insurance policy, or even as an excuse to delay getting one, as it wouldn't come close to meeting your families needs were you to die in the near future.

(Added: OK, maybe pennies is an exageration. Someone aged 25-34 has about a 1 in 2000 chance of dying in the next 12 months (linky), so the cost of providing £15K of life insurance for them for 12 months would be in the region of £7.50 - maybe a bit lower if some people lose the paperwork and their families never claim on them when they die. Still cheap enough to provide as a marketing gimmick - you'd only need a small percentage of customers to sign up for a proper insurance policy with you to make it worthwhile)