If you are just asking the question that means it has not been agreed so by default your job = your plan

If you are obstructing the public highway (road or footpath) you should be discussing this with the council before any works are started remembering that Fire Engine or ambulance are wider than an ordinary car.

You need to consider the following;

As said above by Roundtuit your first point of reference is the Local Authority for the necessary license and/or street works notice.  This may be in two parts; one for the lifting equipment on the highway and one for the use of the highway for works.  This assumes that your organisation is not a Statutory Undertaker and cannot raise a notice yourselves. 

The TM plan is usually a requirement of the LA license and is issued to them with copies of relevant insurances and accreditation to manage works on the highway (including use of the lifting equipment). 

The LA is not necessarily concerned with who produces the TM plan as long as it meets their requirements for scale, colour and key and is drawn up with the relevant competency.  If neither you nor the hire company are qualified to do this, then it would be worth procuring a TM company to manage this element of the works.  This would include drawings, setting up the TM, monitoring it and demobilising.

Street works qualifications are covered under NRSWA, however  most TM companies will work to UK Sector Schemes which are more encompassing and cover more complex scenarios including high speed roads and complex arrangements. 

The TM plan is only part of the management arrangements – you will need to demonstrate why the TM solution you have opted for is suitable on the basis of:

Road widths

Footway widths

Traffic (pedestrians, cyclists, cars, buses etc.)

Several other points of consideration documented within the Street works Code of Practice.