Yeah it is weird that your link is not providing any information about why they did it. I would say the Wikipedia has a better text about it, while also not going to deep:

https://en.m.wikipedia.org/wiki/SS_Exodus

Your first have to understand the territorial occupations at the time of 1946 and who was invested in the region. After the ottoman empire fell Britain gained foot in the area of palestine around 1919. It was only possible by a coalition with the Arab neighbors in the region that were more fond of the british than the ottoman disarray.

https://en.wikipedia.org/wiki/Mandatory_Palestine

After WW2, Britain had a big interest in keeping this area in control and not further develop conflicts in the area by the refugee of jewish people coming from the european camps, that would clash with the coalition partners from the arab countries in the region. The efforts made to create a jewish state was mostly driven by the US, and not britain:

In 1947, the UN adopted a partition plan for a two-state solution in the remaining territory of the mandate. The plan was accepted by the Jewish leadership but rejected by the Arab leaders, and Britain refused to implement the plan. On the eve of final British withdrawal, the Jewish Agency for Israel, headed by David Ben-Gurion, declared the establishment of the State of Israel according to the proposed UN plan.

(https://en.wikipedia.org/wiki/History_of_Palestine)

You can see how britain lost control of the whole region the moment they gave in. Up until this moment they were still hoping to keep the jews out and keep the control of the country. That is the reason they blocked the Exodus. There is also a good take on the SS Exodus Article on britains stance until the caved into the UN Mandate:

Britain’s position was summed up by John Coulson, a diplomat at the British Embassy in Paris, in a message to the Foreign Office in London in August 1947: “You will realize that an announcement of decision to send immigrants back to Germany will produce violent hostile outburst in the press. … Our opponents in France, and I dare say in other countries, have made great play with the fact that these immigrants were being kept behind barbed wire, in concentration camps and guarded by Germans.”[56] Coulson advised that Britain apply as best they could a counter-spin to the story: “If we decide it is convenient not to keep them in camps any longer, I suggest that we should make some play that we are releasing them from all restraint of this kind in accordance with their wishes and that they were only put in such accommodation for the preliminary necessities of screening and maintenance.”[57] The mission of bringing the Jewish refugees of Exodus 1947 back to Germany was known in diplomatic and military circles as “Operation Oasis.”[55]