The first thing to do with burst pipes is turn off the mains stopcock.
This will stop any more water coming into the house, and reduce the pressure of the leak.
However, if the attic cold water storage tank is full then there could still be quite a lot more water to flow out, so opening all other taps will probably help in reducing the amount coming from the leak.
Get buckets etc to catch any remaining water coming out, and then deal with any flood water and damage.
You should also know where the hot and cold down service valves are. They are usually in the hot press or attic. Make sure they work.
If you are unsure of the whereabouts of any of these valves or stopcocks, ask your plumber next time he visits. He'll be more than happy to advise.
If there is any significant damage to furnishings, it's worth taking pictures for insurance purposes!
Cutting out the burst section and fitting a new section of pipe yourself is not really feasible for anyone other than the very competent DIY enthusiast who understands plumbing joints etc. So this will be a job for the plumber.
Hopefully the pipe will be visible, or simply behind a kitchen unit or in the attic where it is still reasonably accessible. In which case the plumber will be able to cut in a new length of pipe quickly and efficiently - they've done it thousands of times before! Clear everything away before they arrive and make as much room as possible for them to operate in.