Hello! Interesting question, let me see if I can help :)

The first thing we should clear up is what the scene from Downton Abbey seems to be implying- that the class separation would naturally result in favoring who had a chance at survival. This absolutely is not true. Class had nothing to do with the order of evacuation. This is a bit of bad history, formed from misunderstanding how and why people were evacuated combined with Titanic as an easy target to critique the rigid class system in which she existed in- that is, Titanic being used as a symbol/metaphor instead of history.

With that cleared up, let’s look at the broad answer to your question- relief for middle/lower class people in the wake of the sinking, followed by more specific examples from the upper class.

General knowledge of the Titanic disaster ends with the arrival of Carpathia into New York on the 18th. However, the legal fallout from Titanic wouldn’t be put to bed until 1916. The White Star Line was sued for billions of dollars (in today’s money) on two continents, but were able to whittle that down to around $650,000, divided up among all the claimants. For context, Charlotte Cadeza claimed almost $200,000 for her luggage alone. The claims were fought down to the penny.

For some, this worked … sort of. Stephen Blackwell’s will valued his estate at around $200,000. His family received a little over $30,000.

On the other hand, Bridget Moran lost everything and after claiming an estate of about $30,000 walked out with a measly $500 which took four years to get. Patrick Ryan's father received $125 for the loss of his son.

As the courts on both sides of the Atlantic began the arduous process of fighting out the tiny details of every claim (is the loss of this $2 hair clip really our fault?), those left lost, destitute, widowed, or orphaned need immediate assistance. Enter the Titanic Relief Fund, established by Lord Mayor of London, David Burnett.

The Titanic Relief Fund was completely funded by donations, and raised millions for everything from school supplies, to headstones. They operated well into the 50's, paying weekly allowances, and covering expenses for those survivors unable to do so. The widow of engineer William Duffy received a new set of dentures in the summer of 1913, the mother of steward William Kerley received glasses and medical care for her bronchitis as well as 3 pounds a week assistance through 1924, Annie Penrose also received 3 pounds a week until 1915 when it was then renewed for another three years. School fees and apprenticeships were paid for by the donations of thousands, eventually forcing the TRF to expand across all of England. In the US, the Examiner Titanic Fund out of Chicago gave survivors Annie Kelly and Annie McGowan each $20 and a trip to the sanatorium to help them deal with their shock and PTSD. Annie Kelly was also given $25 by the WSL for her ordeal- and made to sign a document saying she wouldn't sue them later.

Charity was the only thing keeping the families of the lost afloat in the immediate aftermath of the sinking, as WSL battled survivors in court and the very wealthy tried to sue for the loss of all future income. But from within, and to answer your question more directly, came several personal donations from survivor to survivor.

First Class passenger Margaret Hayes, took care of the Navratil orphans in her home while the search proceeded for their relations (they were kidnapped and sailing under the name Hoffman). Bruce Ismay, managing director, donated $50,000 to the pension fund for crew widows, and in the 20's established a permanent fund for victims of sea disasters, seeding it with his own $125,000.

Harvard University found this was a great time to solicit donations for a new library from Eleanor Widener, who had lost both her husband and son. Mrs. Widener donated 2 million for the new construction named after her son. To this day, the Harry Widener Library at Harvard still places fresh flowers under his memorial plaque.

But, in some cases, generosity became cause of attack. The Duff Gordons, passengers in the scarcely filled lifeboat #1 (12 people), offered each of the seven crew members in their boat 5 pounds for a new kit, as all belongings and pay were officially lost when Titanic sank. Soon, the press frenzy turned this into stories of bribery- first to get off Titanic and later to stop the boat from turning back to pick up survivors. Such was the pushback for Duff Gordon's offer that he was called to testify at the British Inquiry as to whether he had tried to bribe the crew. They were the only passengers called.

A month later, Lady Duff Gordon wrote a letter complaining of the neverending brutal press painting their offer as bribery. She had no idea of knowing that the rumors would never full let them be, that their offer to help the crew of their boat start anew would be defined as rich paying so poor have to die.

Although, Sir Cosmo may not have helped his own case. In his testimony to the Inquiry he stated this his wife's reaction to seeing Titanic sink was to turn to her maid and say "There goes your beautiful nightdress, gone". Context may be key here, but it certainly didn't help them portray sensitivity.

While we have decent records of the Titanic Relief Funds output, much of their input is lost to history. We know certain actions taken by certain first class passengers, but the victims of lesser means, abandoned by the company, were taken care of by the public.