It is an offence to use a vehicle of MOT test age that doesn't have a current test certificate on a public road.
Yes, you can drive a car to a pre-booked MOT test without a valid MOT certificate, even if it is on SORN and doesn't have car tax. The vehicle must have insurance and you should check the policy is valid for driving without an MOT, as some insurers may not cover vehicles under these circumstances.
If it's a non dangerous fault and your previous MOT hasn't expired you can drive it away. If the previous MOT has expired you can't drive it away unless taking it directly elsewhere to be repaired and/or retested.
You can be fined up to £1,000 for driving a vehicle without a valid MOT. You can get an MOT up to a month (minus a day) before it runs out and keep the same renewal date. If your MOT runs out on 15 May, the earliest you can get an MOT to keep the same renewal date for next year is 16 April.
If you get to within 10 days of the expiry date of your tax and you have been unable to secure an MOT appointment or your tax has expired, fill in the short notice appointment request form(external link opens in a new window / tab) . You will need to give the following information: vehicle registration number.
And no, obviously you cannot drive your car. You can only drive it directly the the garage doing the MOT for a pre-booked appointment.
You have until midnight on your MOT's current expiry date to renew it without penalties. If your MOT has expired, remember that it is illegal to continue driving – unless you're heading to a pre-booked MOT appointment.