Lets imagine Gen Douglas Haig doesn't authorized the disasterous Somme Campaign that wiped out the best and brightest soldiers from the British Units. I think with those soldiers who were saved from a certain death, Britain could have continued their tank program unimpeded and launced a campaign in 1917 or even 1918 with tanks used as shields to screen Allied advances. How does keeping the cream of the crop alive affect the BEF's ability to conduct operations for the rest of the war? And we all know about the complete incompetence of the BEF generalship but would better leadership have won the battle or was the Somme a completely inept asinine calamity that was doomed to failure?
The BEF was the majority of the regular British Army before the war. The BEF took heavy casualties in 1914, and by 1916, the original BEF soldiers were largely dead or disabled. Even if the same unit numbers are used, they are not really the same units. The pre-war cream of the British empire was largely destroyed "saving" France in 1914. Many of the troops at the Somme were green, and few are what can be called elite.
If no Somme, then the British have to learn the lesson at another battle, presumably in 1917 in your proposed offensive, so the 1917 offensive actually likely performs worse. The British attack at the Somme was to relieve pressure on the French. The Germans constantly moved troops around by rail, so they will have more troops to use elsewhere. The Somme overlaps Verdun offensive and the Brusilov offensive. If used in Verdun, then the losses are just transferred to France. If used to counter the Brusilov offensive, then the Russian advance may be stopped. The max upside departure for this is 400,000 fewer A-H prisoners and a lot more Russian casualties. Also, Romania may not join the war on the Entente side without a Brusilov victory. So net, net. British have a lot more green troops. And either France or Russia is much weaker with a bonus potential of Romania not entering the war and A-H having two more full armies for 1917 and 1918. Doing nothing for a full year is rarely the correct answer in a hot war. The Somme was a disaster for the British, but doing nothing could have been far worse. You fight a war with the army you have, not the army you would like to have.