Welcome to the site and congrats on your new lotty from another N Yorks gardener!
I would first double check whether, underneath all that grass, there is any terracing or edged beds. These will be trip hazards but could also provide some structure.
I would not take a lawn mower to grass of that length. Use the strimmer to reduce the height of the grass, having done your due diligence beforehand to ensure you've moved any items out of the way.
Good luck! Although it looks bad now, you've got the luxury of time ahead of the winter weather to decide how to get on top of it and make a decent start.