HD.. thanks for confusing the issue... having knocked my statement, why not give an answer to the original question?
I never meant to infer that an ATCO needs a radar to be able to allocate a heading... and are you telling me that the Director at LHR does the job without a radar in front of him/her?... I doubt it.
So although the heading they give may be "off the top of the head" it surely is based on interpretation of the prevailing radar picture and done in the knowledge that the situation can be monitored and recovered. The allocation of headings without any radar monitoring is, IMHO, a last ditch measure, and does not come under the heading of Air Traffic CONTROL... (maybe it was done more in the past?)