Sir,
1. You can deposit contribution under ESI Act, 1948 in the same way as you are making in respect of your HO employees located at Bangalore or at Mumbai. The only difference will be that you will be required to make the contribution separately in respect of Mumbai Branch Office, quoting therein necessary particulars of said Branch Office and Sub-Code Number and submit the returns of contributions etc. separately to the appropriate Regional/Sub/Divisional Office as well as Branch Office of ESIC at Mumbai to which your Branch at Mumbai is attached.
2. However, at present online procedure for payment of contribution, submission of returns etc. has also been introduced and I think, you can ask your Branch Office Manager/Incharge to contact the concerned Branch Office of ESIC at Mumbai to which your said Branch is attached and confirm all such formalities on the subject.
3. In addition to payment of contributions in respect of Branch Office, Mumbai employees, the compliance in respect of obtaining of Insurance numbers, Identity Cards, Family Identity Cards and submission of Accident Report, if such eventuality arises, etc. in respect of Mumbai Branch employees is to be done at Mumbai office itself. Therefore, though you can pay contribution and submit returns from Bangalore, but other formalities as mentioned above are required to be done locally at Mumbai so that the employees of your Branch Office may be able to get benefits under said Act.