Vectorized indexing cell array

I have several (5000+) pressure-time histories in a cell array Data. Each cell in the Data array holds a two column vector of time and pressure. However, the times may be different, and the length of the vector may be different. I currently do this:

(read in all the data files in to the Data cell array)

Times = [];
for index = 1 : numel(file_list)
    Times = [Times ; Data{index}(:,1)];
end
Times = unique(Times);
%  Interpolate on to consistent time base
Press_all = zeros(length(Times), numel(file_list));
for index = 1 : numel(file_list)
    Press_all(:,index) = interp1(Data{index}(:,1), Data{index}(:,2), Times);
end

Is there a better way, or a way to vectorize this? I would like to eliminate the for loops and do something like:

Times = unique(Data{1 : numel(file_list)}(:,1));

Except that the first : does not work.

And then maybe even:

Press_all = interp1(Data{1 : numel(file_list)}(:,1), Data{1 : numel(file_list)}(:,2), Times);

, although that may be pushing things a bit too far.

Thanks for any input