Go in first with £197k.
You'll probably be called back within 20 minutes with a refusal -- during which time the agent probably set the phone down, twiddled their thumbs, then called you back to say the vendor refused.
You then say that you need to think about it further, and will get back to them.
Around and hour or two later, call them back and offer £205k. It might take them a little while this time as they'll actually check with her.
If it's a refusal, tell them that you're not willing to go higher at this point in time, as there are other properties you're interested in that you wish to go begin negotiations on.
It's a given they'll then call you repeatedly over the next couple of days to see how you're feeling about it. Drag it on, telling them you haven't exactly given up, but things are looking good and not progressing so slowly on a different property at a similar price.
If they haven't relented, tell them (flippantly during the conversation) that the last you'll be willing to jump to on this one is £212k, if they can guarantee a quick turnover of the property.
Job done. Or, you walk away at this point because she's a stubborn bitch.