In the circumstances: no, the British Expeditionary Force could not have been any larger. It comprised virtually all the available trained and equipped Army formations at the time; a few more Divisions could theoretically have been scraped together from troops based overseas but that would leave the Empire defenceless, never a viable proposition.

Any significant difference would have required a fundamentally different interwar policy. For various reasons the Army had the lowest priority for funding - a dread of a repeat of the death toll of the First World War, faith in the defensive strength of France, a return to the more traditional focus on the Navy coupled with the new threats and opportunities afforded by air warfare. The Air Force received the lion's share of funds due in no small part to fears of a colossal 'knock-out blow', a devastating aerial attack that could bring a country down in a matter of days.

Even as late as 1938 there were hopes that a continental commitment of land forces might be avoided entirely. In the wake of the Munich crisis the growing threat of war finally prompted plans to expand the Army to 32, then 55, divisions, but these had barely started by the time war was declared. As it was the forces committed were in poor shape for combat; "... the first four divisions of the Field Force went to France inadequately trained and short of every type of equipment, especially guns, ammunition and tanks. The remainder of the Territorial units at home were little more than a token force of semi-trained troops, lacking equipment for realistic training." (Brian Bond, The Battle for France & Flanders: Sixty Years On). Lieutenant-General Alan Brooke, commander of 2 Corps, wrote at the end of November: "On arrival in this country and for the first 2 months the Corps was quite unfit for war, practically in every aspect. Even now our anti-tank gunners are untrained and a large proportion of our artillery have never fired either their equipment or type of smoke shell that they are armed with. To send untrained troops into modern war is courting disaster such as befell the Poles. I only hope that we may now be left in peace for the next 2 to 3 months to complete the required readiness for war" (Alanbrooke War Diaries, 1939-1945).

The eight months of the phony war allowed for slight improvements in training and equipment and foundations for a larger Army but expansion plans would have had to be enacted years earlier to have any effect in September 1939.

Daniel Todman's Britain's War: Into Battle, 1937-1941 and Alan Allport's Britain At Bay: The Epic Story of the Second World War, 1938-1941 are both excellent on the wider situation, specifically on military policy there's Brian Bond's British Military Policy between the Two World Wars.