[Pepperpincushion]

I have a smallish bed in front of one of the windows at the front of my house. It had a hedge in it but it has become over run with brambles. I have started clearing it - just chopping everything down to a low level - and my plan is to remove as much as possible then use a chemical treatment to kill off the remainder. Any recommendations of what would be best for this?
Then I need to replace something there. I want it to be fairly easy to grow, cheap and not too big - I don't want it any higher than about 2.5 feet. Could anyone suggest a good plant for this? The area gets a reasonable amount of sun and I would say the soil is OK - not fabulous but not too awful!

[Paul Plots]

How far away from the house / window was the old hedge?

I guess you will need to dig out the roots and improve the soil if you want to replant another hedge.

[Pepperpincushion]

It is directly beneath the window and about 3 ft deep.

[JayG]

Agree with Paul - don't see how you can replant anything with the existing hedge and bramble roots still in the soil.

I quite unintentionally created a low hedge in my front garden from about 3 different types of variegated euonymus plants rescued from the back garden. I planted them a few feet apart and they've knitted together to from a very pretty, evergreen low hedge which only needs one light trim every year now that it's reached the required height (about 2 1/2 feet.) They don't seem at all fussy about soil or position (poor and North-facing respectively) and get no special treatment at all. 

[Pepperpincushion]

That sounds nice (the Euonymus, not the digging - but I guess that will have to be done!) looks about the right size and seems quite reasonable to buy.

[Paul Plots]

That sounds nice (the Euonymus, not the digging - but I guess that will have to be done!) looks about the right size and seems quite reasonable to buy.

It will be worth adding *something to improve the soil as they will be in there for a fair time.  (*JayG will have some advice for you on that one I expect  )

Give them space for air circulation and not too close to the wall so the roots get wet when it rains.

Good luck with the digging.