Best thing for cutting lawns on slopes are hover mowers, but what size is the area you want to plant, is it full sun, shade, partial shade, what part of the country are you in, exposed and windy or sheltered, and do you know the aspect - north, south...?

Size is approx. .10x8 Mts., East facing, so exposed to both E and NE weather,which, here in the east coast of the Highlands the winds can be quite prolonged at times. Due to surrounding 2story flats the lawn is in partial shade,and because I suffer from TMB ( to many birthdays) even my hover mower appears to get larger and heavier each time hense my thoughts of low maintainance ground cover.

TMB, oh yes, I know that one only too well... I think this needs careful consideration on your part - covering a slope with ivy isn't the end of it - it will need weeding initially, and eventually will spread probably much further than you want and will need cutting back and down - if there's anything vertical nearby, the ivy will head for that as well and climb up. Until it gets dense enough (say 4-6 inches deep complete cover) weeds will germinate in the soil between branches. If TMB is a problem for mowing, I'm assuming it may be even more of a problem when it comes to regular hoeing, weeding and cutting back on a slope, so the question is, is grass more low maintenance than 'low maintenance' planting, and the answer is yes, it is - if you can find a way of cutting it easily. Robotic mowers come to mind, but they're not cheap and the gradient may be too much for one of those anyway; is there a local person you could pay a small amount to come round and cut it regularly during the growing season?

I can't visualise how steep the slope is, but probably the best and likely most attractive easy care solution is some hard surfacing (paving) with two or three areas left open for plants, but again, most of the cost of that will be in the paving. It would, though, reduce maintenance ongoing to an absolute minimum - I'm not going to list plants suitable for that kind of layout unless you think you might want to take that option.

With the caveat that exposing the whole area by removing the grass and planting ground cover will involve maintenance (weeding etc) have a look at Cotoneaster 'Queen of Carpets' - bone hardy, spreads widely, fairly dense cover after 3-5 years, small white flowers in spring (much loved by bees) followed by red berries. Link below for more info on this plant

https://www.rhs.org.uk/Plants/60414/Cotoneaster-procumbens-Queen-of-Carpets/Details

For the shadier parts, Pachysandra terminalis - you'd need to start with a fair number of plants, it can be slow to get going and spread. Alternatively, (or as well) Sarcococca hookeriana is definitely worth considering - hardy down to -15, evergreen, produces suckers so it spreads, see link here

https://www.rhs.org.uk/Plants/65567/Sarcococca-hookeriana-var-digyna-Purple-Stem/Details

You'd need several plants of each type to get any kind of good cover within five years.

Artificial turf is also something you might consider - on a slope, though, it would be best to use a professional company to have it done. There are some good, natural looking ones available now - you'd only know they were artificial if you walked on them (they crunch, like frosty grass does), or if you look closely in bright sunlight, when it 'sparkles' a bit! Laid properly by a professional, it should be almost entirely maintenance free.

Thanks for the advice Bamboo. It looks like I have some thinking to do.