There is no problem having the DNO's earthing terminal connected to MET at the same time as your own earth electrode (just like extraneous-conductive-parts). In fact, a consumer's supplementary earth electrode is recognized by BS 7671. See Fig 3.9 and the descriptions below it.

What you MUST NOT do is connect N to PE within your installation (downstream of the DNO's service head), without disconnecting the distributor's neutral first - regardless of whether the supply is TN-C-S (PME), TN-S, or TT. This is not only an issue for protective devices, but also potentially contravenes ESQCR.

It's absolutely fine for the appropriate switching devices (island mode isolator to disconnect the distributor's live conductors, all lines and Neutral and the N-E bond relay to form TN-S when the grid is fully disconnected) to be part of the inverter, battery management system, etc., provided they meet these requirements.

You will, of course, need to provide the additional consumer earth electrode if one is not already present. The value of electrode resistance required will depend on the size of RCD used for the island-mode circuits ("essential loads") and whether there are any other complications such as TT-d outbuildings or EV charging points.

You must ensure that protection against electric shock and overcurrent are available in all modes of operation.

Because an EESS charges the battery as well as as discharging it, you will need to check the rating of the CU is not exceeded. For example, if the CU is rated for 100 A, and there's a 100 A service fuse, and a 16 A output battery storage system - by feeding 16 A in at one end through an OCPD, because that OCPD gets hot it contributes to the total heat load in the CU - therefore the CU should be rated for 116 A.

All of this is covered in the IET Code of Practice for Electrical Energy Storage Systems.

There is no problem having the DNO's earthing terminal connected to MET at the same time as your own earth electrode (just like extraneous-conductive-parts). In fact, a consumer's supplementary earth electrode is recognized by BS 7671. See Fig 3.9 and the descriptions below it.

What you MUST NOT do is connect N to PE within your installation (downstream of the DNO's service head), without disconnecting the distributor's neutral first - regardless of whether the supply is TN-C-S (PME), TN-S, or TT. This is not only an issue for protective devices, but also potentially contravenes ESQCR.

It's absolutely fine for the appropriate switching devices (island mode isolator to disconnect the distributor's live conductors, all lines and Neutral and the N-E bond relay to form TN-S when the grid is fully disconnected) to be part of the inverter, battery management system, etc., provided they meet these requirements.

You will, of course, need to provide the additional consumer earth electrode if one is not already present. The value of electrode resistance required will depend on the size of RCD used for the island-mode circuits ("essential loads") and whether there are any other complications such as TT-d outbuildings or EV charging points.

You must ensure that protection against electric shock and overcurrent are available in all modes of operation.

Because an EESS charges the battery as well as as discharging it, you will need to check the rating of the CU is not exceeded. For example, if the CU is rated for 100 A, and there's a 100 A service fuse, and a 16 A output battery storage system - by feeding 16 A in at one end through an OCPD, because that OCPD gets hot it contributes to the total heat load in the CU - therefore the CU should be rated for 116 A.

All of this is covered in the IET Code of Practice for Electrical Energy Storage Systems.