Both example sentences have two finite verbs:

He is demanding £5,000 from the elderly woman *whom has ruined his life.

 

Mr Reynolds is highly critical of journalists, *whom just use labels to describe him.

In both cases, there is a relative clause with a second subject before the second finite verb. "Whom" shouldn't be used as a subject¹, so it should be "who".

Corrected, the sentences are:

He is demanding £5,000 from the elderly woman who has ruined his life.

 

Mr Reynolds is highly critical of journalists, who just use labels to describe him.

Most people don't use "whom" at all, except in certain well known phrases such as "To whom it may concern", so in most environments you can always use "who" instead of "whom".

¹ In my sentence, "Whom" substitutes for "The word 'whom'", so it is grammatically correct.

Both example sentences have two finite verbs:

He is demanding £5,000 from the elderly woman *whom has ruined his life.

Mr Reynolds is highly critical of journalists, *whom just use labels to describe him.

In both cases, there is a relative clause with a second subject before the second finite verb. "Whom" shouldn't be used as a subject¹, so it should be "who".

Corrected, the sentences are:

He is demanding £5,000 from the elderly woman who has ruined his life.

Mr Reynolds is highly critical of journalists, who just use labels to describe him.

Most people don't use "whom" at all, except in certain well known phrases such as "To whom it may concern", so in most environments you can always use "who" instead of "whom".

¹ In my sentence, "Whom" substitutes for "The word 'whom'", so it is grammatically correct.