My take is that that would probably only apply to land with holding numbers. For grazing neighbours lawns, you would definitely need to contact DEFRA or SEERAD to find out the rules, as they will not have holding numbers and it is likely to be the case that you cannot graze them on land which is not registered as a holding. Also, the animals would need to stay in each area until the standstill had passed ie 6 days in England, 13 days in Scotland. With pigs, apparently you can get a 'walking license' so you can take them along a predetermined route off the holding for a regular walk, but I have not heard of that for sheep.
You could also find problems with poisonous garden plants and a lack of fencing in domestic gardens.