This is a grey area when it comes to insurance (as are most things with insurance, if they don't want to pay out, they just don't mention it in the policy wording, so they can moan about it in the event of a claim). First thing would be to check both companies policy documents / wording - even the tiny print (you can normally do this on the respective websites before you buy). See if it says under
"what is not covered", something like;
"any claim arising while there is another insurance policy in place" - then clearly you can't do it with that company. Otherwise the Law only states in order to drive, you must have insurance against third party risks, therefore;
While driving, your Dad would be covered by his policy.
While driving, you would be covered by your policy.
As Liam says above, the problems would arise if you needed to make a claim that didn't involve a driver, where it is clear whose policy should cover it, such as theft or damage while it is parked up.
If you are both fully comp (or covered for theft), then the insurers
should halve the costs for a total loss or theft claim between them. They would look at their policy wording very carefully though, and try and void it if you haven't declared everything as it should be (registered keeper, annual mileage etc). And there are downsides to that too, as in you would both lose any No Claims Discount against you.
It's definitely not illegal, it just might be hassle trying to get them to pay out between them both in the event of a non third party claim.
Read both policies wording very very carefully
glitch on confused.com?
phone any insurance company and ask them... for the reasons i said above 
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