One who reckons that Cockney lady's a drunk? (8)

'one who reckons' is the definition.
The definition suggests a singular noun which matches the answer.

'cockney lady's a drunk?' is the wordplay.
I cannot really see how this works, but
'cockney lady' could be 'er' ('her' with the 'h' dropped) and 'er' is found within the answer.
The remaining letters 'totter' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

'that' acts as a link.

Can you help me to learn more?