"Technically" you could be insured on the Type R under your own policy if it includes cover to drive other cars (be that 3rd party or fully comprehensive cover) - that is indeed provided that the Type R is NOT in your name, or your wife's name, or registered at the same address as your policy and you can make a clear case you do not have regular access (because if you do then the insurance company will just argue that it really is your car to start with and not pay out if something happens). That last part about the address and "regular access" has been added by most insurance companies in the past 2 years or so - but best to check with your own policy fine-print to be sure.
However, as pointed out, even if you think you are covered... the insurance company will more than likely (try to) find a reason not to honour your cover. Also... if there is no actual policy on the Type R then if it gets stolen, goes on fire, or is otherwise damaged you will not be covered and lets face it these cars are now worth real money. For these reasons it really is not advisable to rely on "possible technicalities" to "maybe" be (partially) insured.
The most cost effective solutions which will afford you full cover on your Type R:
1) seeing you have a daily driver with its own insurance policy you can then insure the Type R under a "classic" car policy. There are several companies that provide this type of cover and it is more cost effective than a normal 2nd policy.
2) alternative you can get trade insurance (for a garage), or fleet insurance. This type of policy will allow you to drive any car you personally own. It is normally a little more expensive than a single normal policy, but cheaper than 2 separate policies.
3) there are a few bigger insurance companies who are willing to "mirror" your no claims bonus of your first policy onto a 2nd policy to cover a 2nd car. What this means is that they will "copy" your no claims bonus from your 1st policy onto the 2nd policy. This way you can get quite a good price on the 2nd policy - provided you have a lot of no claims bonus built up already. I used to have this with AXA, but there may be others who also offer this.