The answer is ‘YES – BUT’ … it is hedged around with some important restrictions, the main one being that HCbE should only take place with the express approval of the bishop and even then, only for a limited time.
This is from the Guidelines issued by the House of Bishops (I have highlighted some of the points):
The practice of Communion by Extension as envisaged by the authorized service has some affinities with the communion of the sick, from elements which have been consecrated at a celebration in church. The main differences concern the public nature of Communion by Extension, and the consequent need for careful attention to the overall shape and content of the service. For this reason it is required that the service should be led only by a person who has been specifically authorized for this purpose by the bishop. Such a person will normally be a deacon, Reader or lay worker licensed under Canon E 7, and must wear the appropriate vesture.
Paragraphs 4, 5 and 6:
The service of Communion by Extension has been drawn up to make clear that it is not in itself a celebration of Holy Communion, and yet enables a worshipping community to participate in Holy Communion ‘by extension’. When it is introduced to a congregation care should be taken to explain the close relationship between the two services; there is but one celebration of Holy Communion, from which the consecrated elements are brought.
5 The notes which accompany the service make clear that explicit permission must be obtained from the bishop for the use of this rite, and that such permission should relate to specific pastoral circumstances. Such permission will normally be in writing, and will be either for a particular occasion or for a limited duration. The bishop should regularly review the use of this rite in parishes where it is used. Communion by Extension must always be regarded as exceptional and provisional, looking to circumstances when a priest will be available to preside at a celebration of Holy Communion.
6 Communion by Extension will require that special care is given to the conduct of the service, and especially that the consecrated elements are treated in a seemly and dignified manner. Those responsible for a service should ensure that the consecrated elements are adequate to meet the needs of the congregation, and that any consecrated bread and wine which is not required for the purposes of communion is consumed either during or immediately after the service.
Here is a downloadable version of the order of service for Public Worship with Communion by Extension https://www.churchofengland.org/sites/default/files/2017-11/Public%20Worship%20with%20Communion%20by%20Extension.pdf
You can also of course get this ordered from Church House Publishing.
If in any doubt, refer to your bishop, archdeacon or rural/area dean. The one thing that is abundantly clear is that we are not free simply to make use of this service at any time, but must have permission.
A local example of a time and place when HCbE was used: http://www.saintandrewsshottery.org/services/holy-communion-by-extension.php