You have to get your 4 weeks notice. If you work your notice, you're entitled to be paid for it. If you cannot work your notice, and there is no provision in your contract to be paid while on sick leave, then you won't get paid. You may however be entitled to Illness Benefit if you have the stamps, although presumably if you did, you would already be receiving that.
It would be a different matter if you could work, but were not being asked to, or if you weren't given 4 weeks notice, in which case you would be entitled to pay in lieu of that notice.
Basically if he didn't give you the opportunity to work your notice, you're entitled to be paid for it. If he did, and you weren't able to take up that offer, then you're not. Also, if you're entitled to paid sick leave under your contract, then you'd be entitled to paid notice.