We report deep EVN and eMERLIN observations of the Type Ia SN 2014J in the nearby galaxy M 82 . Our observations represent , together with JVLA observations of SNe 2011fe and 2014J , the most sensitive radio studies of Type Ia SNe ever . By combining data and a proper modeling of the radio emission , we constrain the mass-loss rate from the progenitor system of SN 2014J to \dot { M } \lesssim 7.0 \times 10 ^ { -10 } ~ { } \mbox { $ { M _ { \odot } yr ^ { -1 } } $ } ( for a wind speed of 100 \mbox { km s$ { } ^ { -1 } $ } ) . If the medium around the supernova is uniform , then n _ { ISM } \lesssim 1.3 \mbox { cm$ { } ^ { -3 } $ } , which is the most stringent limit for the ( uniform ) density around a Type Ia SN . Our deep upper limits favor a double-degenerate ( DD ) scenario–involving two WD stars–for the progenitor system of SN 2014J , as such systems have less circumstellar gas than our upper limits . By contrast , most single-degenerate ( SD ) scenarios , i.e. , the wide family of progenitor systems where a red giant , main-sequence , or sub-giant star donates mass to a exploding WD , are ruled out by our observations While completing our work , we noticed that a paper by Margutti et al . ( 36 ) was submitted to The Astrophysical Journal . From a non-detection of X-ray emission from SN 2014J , the authors obtain limits of \dot { M } \phantom { \leq } \smash { \buildrel \over { \lower 2.675022 pt \hbox { $% \buildrel \lower 2.140017 pt \hbox { $ \displaystyle < $ } \over { \sim } $ } } } 1.2 \times 1 % 0 ^ { -9 } { M _ { \odot } yr ^ { -1 } } ( for a wind speed of 100 \mbox { km s$ { } ^ { -1 } $ } ) and n _ { ISM } \phantom { \leq } \smash { \buildrel \over { \lower 2.675022 pt \hbox { $% \buildrel \lower 2.140017 pt \hbox { $ \displaystyle < $ } \over { \sim } $ } } } 3.5 \mbox { % cm$ { } ^ { -3 } $ } , for the \rho \propto r ^ { -2 } wind and constant density cases , respectively . As these limits are less constraining than ours , the findings by Margutti et al . ( 36 ) do not alter our conclusions . The X-ray results are , however , important to rule out free-free and synchrotron self-absorption as a reason for the radio non-detections . . Our estimates on the limits to the gas density surrounding SN2011fe , using the flux density limits from Chomiuk et al . ( 10 ) , agree well with their results . Although we discuss possibilities for a SD scenario to pass observational tests , as well as uncertainties in the modeling of the radio emission , the evidence from SNe 2011fe and 2014J points in the direction of a DD scenario for both .