Individuals attending the hospital to undergo operations are at risk of developing blood clots in the legs, known as deep vein thrombosis (DVT). A clot in the leg can cause swelling, pain, and other long-term problems. If a clot in the leg breaks off and travels to the lungs, it can cause problems with the lungs' ability to move oxygen from the air into the blood and may be life-threatening. This is known as pulmonary embolism (PE). DVT and PE are known collectively as venous thromboembolism or VTE. The importance of preventing VTE in surgical patients is widely recognised, with two main strategies used: thinning the blood with regular injections and/or tablets and wearing elastic stockings to help stop blood from sitting in the leg veins where it can clot. Evidence for using elastic stockings to prevent VTE has recently been challenged. Additionally, there is a lack of evidence for the additional benefit of stockings over and above that of blood thinning medications. If stockings were to reduce VTE over and above blood thinning medication, these benefits need to be weighed against the risks and disadvantages of stockings, including discomfort, restricting blood flow to the leg causing blisters and wounds in addition to the cost. If stockings were found not to reduce the risk of clots, they would no longer need to be used in these patients, thus reducing the disadvantages of stockings, and saving the NHS millions of pounds per year. Certain types of operations (300,000 per year in the UK) are linked with a particularly high risk of VTE, including cancer surgery, surgery in the abdomen and pelvis, and bone (orthopaedic) surgery. In these cases, patients are offered blood thinning medications both during their hospital stay and for a period after they have left the hospital. Furthermore, these patients are offered stockings to wear while in the hospital. It is not known if, in patients who receive blood thinning medications both in hospital and after discharge, the addition of wearing stockings whilst in hospital reduces their risk of VTE any further. The purpose of this study is to investigate if it is worthwhile using stockings, in addition to blood thinning medication, to reduce blood clots after surgery. People enrolled in the study will be those at the highest risk of VTE and require an extended period of medication to reduce the risk of a blood clot. A computer will randomly choose one of the below treatments by chance to make the trial fair: A) Extended duration clot-reducing medicine in addition to stockings B) Extended duration clot-reducing medicine alone The surgery and all the other medical care will continue as normal. Everyone in the study will get an ultrasound scan at 21 - 35 days after their operation to check if they have developed a blood clot. This is an additional scan, not routinely performed in the NHS, to make sure that all blood clots are detected at an early stage. Participants will receive a phone call at 7, 21-35 and 90 days after their treatment to see if they have developed a blood clot or had any problems with the treatment.