Nothing much will grow under privet because it is such a greedy feeder. If you widen the border abut a foot or so and keep the soil well nourished with good compost or at least feed any plants you put there with a good general fertilizer you should do better. Does the border get sun or is it shaded most of the time, and is the soil fairly light or rather heavy?

I did wonder if it was the privet so thank you for confirming my suspicion. The strip of garden is about 15 inches wide, in sun all morning until about 1.00pm. Our soil tends to be heavy and I live on the south coast and it does get windy!
It is a block of flats and the privet hedge was put in when it was built about 14 years ago. It's a thick hedge, with two rows of privet, which the residents would like to remove as there is more garden room behind it. The managing agents only have a small budget for extra garden items. Your answer will help me convince them that we have to take out one row of privet and add lots of fertiliser before plants will grow. Then when they are established we can finally remove the privet! Thanks again.

Removal of a section or all will need considerable muscle. This means that removal won't come cheap. That soil will be hard and compacted due to years of root growth and to get that section ready for planting all the roots must be removed....this is tough stuff and might be as expensive as tree removal. This means that the management might tack on a monthly fee to get up enough scratch to get the job done. Keep that in mind if you do convince them.

Not sure about removing the second row after planting up the border because the privet roots from the second row will be under them so it depends how the privets are removed. We have removed a section of privet hedge and left a lot of the roots in situ and the border is growing well in spite of it. If they try to deal with all the roots by getting them out rather than sawing the thicker ones off (which is what we did) they may need to dig over the entire border.
Privet doesn't send up suckers from roots left in.

Are you dependent on the agents for planting or will you be allowed to do it?

Thank you both. The managing agents are reluctant to take up the privet but we would like something pretty to look at. We are allowed to put plants in and have tried quite a few but they don't survive. The builders planted up the garden with grass, hedging, green shrubs and a few trees although we have a lovely old wall behind the trees. No flowers. So we look out onto green or in winter bare twigs and trunks.
Looks like we have a fight on our hands but thank you for your help.

If you are allowed to widen the border try that. Otherwise how about some containers with bright bedding?

Good idea about the containers! Thanks again.