The full public health regulations which are subject to approval in parliament this evening (4th November 2020) can be found here

Made yesterday at 2.45 pm, they will be laid before parliament at 4.10 pm, then to come into force on the 5th of November.

The highlights from this document relating to moving house and the exceptions for this are as follows;

(g) to undertake any of the following activities in connection with the purchase, sale, letting
or rental of a residential property—
(i) visiting estate or letting agents, developer sales offices or show homes;
(ii) viewing residential properties to look for a property to buy or to rent;
(iii) preparing a residential property to move in;
(iv) moving house;
(v) visiting a residential property to undertake any activities required for the rental or
sale of that property;

In addition;

(j) to visit a waste disposal or recycling centre.