Harder work - but many gardeners swear by the finish on the lawn....:-) Make sure you get one with a grass box.

They are brilliant my dad used one for years when we were younger get with a grass box as Spritz said also keep the bearings etc on the blades well lubricated

Phew, I'd go for a flymo every time, just takes a bit of practice to get the technique right. The circles you're talking about occur when the mower is left too long in one spot, either because it's "stuck" or you've let the power cut off - whenever you stop, or it gets stuck, tip it to the left or the right immediately, till the blade stops turning, and you won't have that trouble again. Advantages with them are they'll cut longer grass, even if its wet, they're light and easy to manouevre, and will cut anything in their path. Disadvantage is no stripes, if you wanted a striped lawn. I also find they're a lot easier to use without the grass collection box, so I never use mine. Most of the grass gets chewed into soggy lumps which are easy to collect afterwards anyway, and most of it is stuck inside the mower.
If you're strong and fit, push along unpowered mowers do a good job, though they don't cut the long, flowering growths of grass if there are any, they'll need to be nipped with shears afterwards. True of cylinder mowers generally, even the electric ones.

Thanks all, especially for the different perspectives. I got going with the rake and autumn feed last night, the poor patch is in a sorry state. My hacking with the flymo didn't help!

The flymo we have inherited is very heavy, and is mostly glued together. We were told it had seen better days but was a work horse.

I think we will be better with the unpowered push model given it is a small area but keep the flymo for when the grass is a bit longer.