Working in India as a trailing husband on spousal visa

This news is from 2012.
Financial Express
I think you can work legally in India on a spouse visa.

As for volunteering, of course you can.
If you are into teaching, you may like to check this organization out. They are based out of Mumbai/Pune area and are doing a good job.
Teach For India

I know many expats living in other countries who work either online or remotely for their off-shore business/es.
Since India and UK have a comprehensive agreement on Double Taxation Avoidance, you only pay Tax once at the source of your income.
If you are earning through PayPal which is connected to your UK a/c, then pay the tax there.
Later transfer the money to your Indian a/c (if you get one) through bank transfer.
I think that should be fair and less complicated.
BTW, I am not an expert on Expat Taxation rules etc., it's just an effort to give you some leads. Hope it helps.

Edit:
Since you are highly qualified in Finance and IT, it won't be a problem for you to land a full-time  job in Mumbai/Pune. You can even change your employer if you want.

Quote from the news above:
"According to a recent change, the spouse of the foreign national who is on secondment to India, can get the dependent visa converted into an employment visa in India on meeting the following conditions: The spouse has a valid employment visa; the spouse satisfies all conditions laid down for grant of employment visa in India; and the application for conversion is supported by a favourable report from jurisdictional Foreigners’ Registration Office.
.......
A foreign national is now permitted to change his employer in India if it is approved by the ministry of home affairs (MHA).
The applications may be considered by MHA if the following mentioned conditions are satisfied: The foreign national holds a senior/skilled position in India; the change of employer is between registered holding company and its subsidiaries or vice-versa or subsidiaries of a registered holding company; and the application is supported by a certificate of holding/subsidiary relationship, a justification letter, and a no-objection certificate, etc."