What factors have contributed to the success in steel framed
construction in the UK and why has growth not been significantly
effected by rising raw steel prices?

It is cheap, rapid to assemble and comparatively light.

The steel is a small proportion of the total cost of build.

Also it looks as if there has been overcapacity in the steel industry.

I am not so sure about the last line:  overcapacity.  I have
understood that the construction boom in China has had an effect on
the world market.

However, in addition and support to Frde's other points, it should be
understood that the lead time on planning major construction is so
long that even the most significant increases in material prices could
only affect  - if at all -  construction in the most initial planning
phase.  And at that stage, those responsible would look at the longer
term price movement for steel and perhaps decided that the present
price will decline by the time they need to order.

@MyOarin

My impression is that there has been overcapacity in Europe for
'non-exotic' steel production - the raw material is dirt cheap so I
doubt that China has had a major influence ... well what I mean is
that China buys raw materials or sophisticated machine tools - not
steel girders.

Good point about the time scale, the high rise office building
scenario in the UK is such that they busily build when office rents
are literally negative.

It does not matter much as such things are typically owned by large
financial institutions who simply 'capitalize' expenditure - a cost
overrun becomes an addition to the balance sheet.

CentrePoint was the first conspicuous 'non yielding asset'